Base class for unsteady solvers. More...

#include <PulseWaveSystem.h>

Inheritance diagram for Nektar::PulseWaveSystem:

Collaboration diagram for Nektar::PulseWaveSystem:

Public Member Functions
virtual	~PulseWaveSystem ()
	Destructor.
int	GetNdomains ()
Array< OneD, MultiRegions::ExpListSharedPtr >	UpdateVessels (void)
void	CalcCharacteristicVariables (int omega)
Public Member Functions inherited from Nektar::SolverUtils::UnsteadySystem
virtual SOLVER_UTILS_EXPORT	~UnsteadySystem ()
	Destructor.
SOLVER_UTILS_EXPORT NekDouble	GetTimeStep (const Array< OneD, const Array< OneD, NekDouble > > &inarray)
	Calculate the larger time-step mantaining the problem stable.
Public Member Functions inherited from Nektar::SolverUtils::EquationSystem
virtual SOLVER_UTILS_EXPORT	~EquationSystem ()
	Destructor.
SOLVER_UTILS_EXPORT void	SetUpTraceNormals (void)
SOLVER_UTILS_EXPORT void	InitObject ()
	Initialises the members of this object.
SOLVER_UTILS_EXPORT void	DoInitialise ()
	Perform any initialisation necessary before solving the problem.
SOLVER_UTILS_EXPORT void	DoSolve ()
	Solve the problem.
SOLVER_UTILS_EXPORT void	TransCoeffToPhys ()
	Transform from coefficient to physical space.
SOLVER_UTILS_EXPORT void	TransPhysToCoeff ()
	Transform from physical to coefficient space.
SOLVER_UTILS_EXPORT void	Output ()
	Perform output operations after solve.
SOLVER_UTILS_EXPORT NekDouble	LinfError (unsigned int field, const Array< OneD, NekDouble > &exactsoln=NullNekDouble1DArray)
	Linf error computation.
SOLVER_UTILS_EXPORT std::string	GetSessionName ()
	Get Session name.
SOLVER_UTILS_EXPORT void	ResetSessionName (std::string newname)
	Reset Session name.
SOLVER_UTILS_EXPORT LibUtilities::SessionReaderSharedPtr	GetSession ()
	Get Session name.
SOLVER_UTILS_EXPORT MultiRegions::ExpListSharedPtr	GetPressure ()
	Get pressure field if available.
SOLVER_UTILS_EXPORT void	PrintSummary (std::ostream &out)
	Print a summary of parameters and solver characteristics.
SOLVER_UTILS_EXPORT void	SetLambda (NekDouble lambda)
	Set parameter m_lambda.
SOLVER_UTILS_EXPORT void	EvaluateFunction (Array< OneD, Array< OneD, NekDouble > > &pArray, std::string pFunctionName, const NekDouble pTime=0.0, const int domain=0)
	Evaluates a function as specified in the session file.
SOLVER_UTILS_EXPORT void	EvaluateFunction (std::vector< std::string > pFieldNames, Array< OneD, Array< OneD, NekDouble > > &pFields, const std::string &pName, const int domain=0)
	Populate given fields with the function from session.
SOLVER_UTILS_EXPORT void	EvaluateFunction (std::vector< std::string > pFieldNames, Array< OneD, MultiRegions::ExpListSharedPtr > &pFields, const std::string &pName, const int domain=0)
	Populate given fields with the function from session.
SOLVER_UTILS_EXPORT void	EvaluateFunction (std::string pFieldName, Array< OneD, NekDouble > &pArray, const std::string &pFunctionName, const NekDouble &pTime=0.0, const int domain=0)
SOLVER_UTILS_EXPORT std::string	DescribeFunction (std::string pFieldName, const std::string &pFunctionName, const int domain)
	Provide a description of a function for a given field name.
SOLVER_UTILS_EXPORT void	InitialiseBaseFlow (Array< OneD, Array< OneD, NekDouble > > &base)
	Perform initialisation of the base flow.
SOLVER_UTILS_EXPORT void	SetInitialConditions (NekDouble initialtime=0.0, bool dumpInitialConditions=true, const int domain=0)
	Initialise the data in the dependent fields.
SOLVER_UTILS_EXPORT void	EvaluateExactSolution (int field, Array< OneD, NekDouble > &outfield, const NekDouble time)
	Evaluates an exact solution.
SOLVER_UTILS_EXPORT NekDouble	L2Error (unsigned int field, const Array< OneD, NekDouble > &exactsoln, bool Normalised=false)
	Compute the L2 error between fields and a given exact solution.
SOLVER_UTILS_EXPORT NekDouble	L2Error (unsigned int field, bool Normalised=false)
	Compute the L2 error of the fields.
SOLVER_UTILS_EXPORT Array < OneD, NekDouble >	ErrorExtraPoints (unsigned int field)
	Compute error (L2 and L_inf) over an larger set of quadrature points return [L2 Linf].
SOLVER_UTILS_EXPORT void	WeakAdvectionGreensDivergenceForm (const Array< OneD, Array< OneD, NekDouble > > &F, Array< OneD, NekDouble > &outarray)
	Compute the inner product $(\nabla \phi \cdot F)$ .
SOLVER_UTILS_EXPORT void	WeakAdvectionDivergenceForm (const Array< OneD, Array< OneD, NekDouble > > &F, Array< OneD, NekDouble > &outarray)
	Compute the inner product $(\phi, \nabla \cdot F)$ .
SOLVER_UTILS_EXPORT void	WeakAdvectionNonConservativeForm (const Array< OneD, Array< OneD, NekDouble > > &V, const Array< OneD, const NekDouble > &u, Array< OneD, NekDouble > &outarray, bool UseContCoeffs=false)
	Compute the inner product $(\phi, V\cdot \nabla u)$ .
f SOLVER_UTILS_EXPORT void	AdvectionNonConservativeForm (const Array< OneD, Array< OneD, NekDouble > > &V, const Array< OneD, const NekDouble > &u, Array< OneD, NekDouble > &outarray, Array< OneD, NekDouble > &wk=NullNekDouble1DArray)
	Compute the non-conservative advection.
SOLVER_UTILS_EXPORT void	WeakDGAdvection (const Array< OneD, Array< OneD, NekDouble > > &InField, Array< OneD, Array< OneD, NekDouble > > &OutField, bool NumericalFluxIncludesNormal=true, bool InFieldIsInPhysSpace=false, int nvariables=0)
	Calculate the weak discontinuous Galerkin advection.
SOLVER_UTILS_EXPORT void	WeakDGDiffusion (const Array< OneD, Array< OneD, NekDouble > > &InField, Array< OneD, Array< OneD, NekDouble > > &OutField, bool NumericalFluxIncludesNormal=true, bool InFieldIsInPhysSpace=false)
	Calculate weak DG Diffusion in the LDG form.
SOLVER_UTILS_EXPORT void	Checkpoint_Output (const int n)
	Write checkpoint file of m_fields.
SOLVER_UTILS_EXPORT void	Checkpoint_Output (const int n, MultiRegions::ExpListSharedPtr &field, std::vector< Array< OneD, NekDouble > > &fieldcoeffs, std::vector< std::string > &variables)
	Write checkpoint file of custom data fields.
SOLVER_UTILS_EXPORT void	WriteFld (const std::string &outname)
	Write field data to the given filename.
SOLVER_UTILS_EXPORT void	WriteFld (const std::string &outname, MultiRegions::ExpListSharedPtr &field, std::vector< Array< OneD, NekDouble > > &fieldcoeffs, std::vector< std::string > &variables)
	Write input fields to the given filename.
SOLVER_UTILS_EXPORT void	ImportFld (const std::string &infile, Array< OneD, MultiRegions::ExpListSharedPtr > &pFields)
	Input field data from the given file.
SOLVER_UTILS_EXPORT void	ImportFldToMultiDomains (const std::string &infile, Array< OneD, MultiRegions::ExpListSharedPtr > &pFields, const int ndomains)
	Input field data from the given file to multiple domains.
SOLVER_UTILS_EXPORT void	ImportFld (const std::string &infile, std::vector< std::string > &fieldStr, Array< OneD, Array< OneD, NekDouble > > &coeffs)
	Output a field. Input field data into array from the given file.
SOLVER_UTILS_EXPORT void	ImportFld (const std::string &infile, MultiRegions::ExpListSharedPtr &pField, std::string &pFieldName)
	Output a field. Input field data into ExpList from the given file.
SOLVER_UTILS_EXPORT void	ScanForHistoryPoints ()
	Builds map of which element holds each history point.
SOLVER_UTILS_EXPORT void	WriteHistoryData (std::ostream &out)
	Probe each history point and write to file.
SOLVER_UTILS_EXPORT void	SessionSummary (SummaryList &vSummary)
	Write out a session summary.
SOLVER_UTILS_EXPORT Array < OneD, MultiRegions::ExpListSharedPtr > &	UpdateFields ()
SOLVER_UTILS_EXPORT LibUtilities::FieldMetaDataMap &	UpdateFieldMetaDataMap ()
	Get hold of FieldInfoMap so it can be updated.
SOLVER_UTILS_EXPORT NekDouble	GetFinalTime ()
	Return final time.
SOLVER_UTILS_EXPORT int	GetNcoeffs ()
SOLVER_UTILS_EXPORT int	GetNcoeffs (const int eid)
SOLVER_UTILS_EXPORT int	GetNumExpModes ()
SOLVER_UTILS_EXPORT const Array< OneD, int >	GetNumExpModesPerExp ()
SOLVER_UTILS_EXPORT int	GetNvariables ()
SOLVER_UTILS_EXPORT const std::string	GetVariable (unsigned int i)
SOLVER_UTILS_EXPORT int	GetTraceTotPoints ()
SOLVER_UTILS_EXPORT int	GetTraceNpoints ()
SOLVER_UTILS_EXPORT int	GetExpSize ()
SOLVER_UTILS_EXPORT int	GetPhys_Offset (int n)
SOLVER_UTILS_EXPORT int	GetCoeff_Offset (int n)
SOLVER_UTILS_EXPORT int	GetTotPoints ()
SOLVER_UTILS_EXPORT int	GetTotPoints (int n)
SOLVER_UTILS_EXPORT int	GetNpoints ()
SOLVER_UTILS_EXPORT int	GetNumElmVelocity ()
SOLVER_UTILS_EXPORT int	GetSteps ()
SOLVER_UTILS_EXPORT NekDouble	GetTimeStep ()
SOLVER_UTILS_EXPORT void	CopyFromPhysField (const int i, Array< OneD, NekDouble > &output)
SOLVER_UTILS_EXPORT void	CopyToPhysField (const int i, Array< OneD, NekDouble > &output)
SOLVER_UTILS_EXPORT void	SetStepsToOne ()
SOLVER_UTILS_EXPORT void	ZeroPhysFields ()
SOLVER_UTILS_EXPORT void	FwdTransFields ()
SOLVER_UTILS_EXPORT void	GetFluxVector (const int i, Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &flux)
SOLVER_UTILS_EXPORT void	GetFluxVector (const int i, Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &fluxX, Array< OneD, Array< OneD, NekDouble > > &fluxY)
SOLVER_UTILS_EXPORT void	GetFluxVector (const int i, const int j, Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &flux)
SOLVER_UTILS_EXPORT void	NumericalFlux (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numflux)
SOLVER_UTILS_EXPORT void	NumericalFlux (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numfluxX, Array< OneD, Array< OneD, NekDouble > > &numfluxY)
SOLVER_UTILS_EXPORT void	NumFluxforScalar (const Array< OneD, Array< OneD, NekDouble > > &ufield, Array< OneD, Array< OneD, Array< OneD, NekDouble > > > &uflux)
SOLVER_UTILS_EXPORT void	NumFluxforVector (const Array< OneD, Array< OneD, NekDouble > > &ufield, Array< OneD, Array< OneD, Array< OneD, NekDouble > > > &qfield, Array< OneD, Array< OneD, NekDouble > > &qflux)
SOLVER_UTILS_EXPORT void	SetModifiedBasis (const bool modbasis)
SOLVER_UTILS_EXPORT int	NoCaseStringCompare (const string &s1, const string &s2)
	Perform a case-insensitive string comparison.

Protected Member Functions
	PulseWaveSystem (const LibUtilities::SessionReaderSharedPtr &m_session)
	Initialises PulseWaveSystem class members.
virtual void	v_InitObject ()
virtual void	v_DoInitialise ()
	Sets up initial conditions.
virtual void	v_DoSolve ()
	Solves an unsteady problem.
void	LinkSubdomains (Array< OneD, Array< OneD, Array< OneD, NekDouble > > > &fields)
	Links the subdomains.
void	BifurcationRiemann (Array< OneD, NekDouble > &Au, Array< OneD, NekDouble > &uu, Array< OneD, NekDouble > &beta, Array< OneD, NekDouble > &A_0)
	Riemann Problem for Bifurcation.
void	MergingRiemann (Array< OneD, NekDouble > &Au, Array< OneD, NekDouble > &uu, Array< OneD, NekDouble > &beta, Array< OneD, NekDouble > &A_0)
	Riemann Problem for Merging Flow.
void	JunctionRiemann (Array< OneD, NekDouble > &Au, Array< OneD, NekDouble > &uu, Array< OneD, NekDouble > &beta, Array< OneD, NekDouble > &A_0)
	Riemann Problem for Junction.
virtual void	v_Output (void)
void	CheckPoint_Output (const int n)
NekDouble	v_L2Error (unsigned int field, const Array< OneD, NekDouble > &exactsoln=NullNekDouble1DArray, bool Normalised=false)
	Compute the L2 error between fields and a given exact solution.
NekDouble	v_LinfError (unsigned int field, const Array< OneD, NekDouble > &exactsoln=NullNekDouble1DArray)
	Compute the L_inf error between fields and a given exact solution.
void	WriteVessels (const std::string &outname)
	Write input fields to the given filename.
void	EnforceInterfaceConditions (const Array< OneD, const Array< OneD, NekDouble > > &fields)
Protected Member Functions inherited from Nektar::SolverUtils::UnsteadySystem
SOLVER_UTILS_EXPORT	UnsteadySystem (const LibUtilities::SessionReaderSharedPtr &pSession)
	Initialises UnsteadySystem class members.
SOLVER_UTILS_EXPORT NekDouble	MaxTimeStepEstimator ()
	Get the maximum timestep estimator for cfl control.
virtual SOLVER_UTILS_EXPORT void	v_GenerateSummary (SummaryList &s)
	Print a summary of time stepping parameters.
virtual SOLVER_UTILS_EXPORT void	v_AppendOutput1D (Array< OneD, Array< OneD, NekDouble > > &solution1D)
	Print the solution at each solution point in a txt file.
virtual SOLVER_UTILS_EXPORT void	v_NumericalFlux (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numflux)
virtual SOLVER_UTILS_EXPORT void	v_NumericalFlux (Array< OneD, Array< OneD, NekDouble > > &physfield, Array< OneD, Array< OneD, NekDouble > > &numfluxX, Array< OneD, Array< OneD, NekDouble > > &numfluxY)
virtual SOLVER_UTILS_EXPORT void	v_NumFluxforScalar (const Array< OneD, Array< OneD, NekDouble > > &ufield, Array< OneD, Array< OneD, Array< OneD, NekDouble > > > &uflux)
virtual SOLVER_UTILS_EXPORT void	v_NumFluxforVector (const Array< OneD, Array< OneD, NekDouble > > &ufield, Array< OneD, Array< OneD, Array< OneD, NekDouble > > > &qfield, Array< OneD, Array< OneD, NekDouble > > &qflux)
virtual SOLVER_UTILS_EXPORT NekDouble	v_GetTimeStep (const Array< OneD, const Array< OneD, NekDouble > > &inarray)
	Return the timestep to be used for the next step in the time-marching loop.
virtual SOLVER_UTILS_EXPORT bool	v_PreIntegrate (int step)
virtual SOLVER_UTILS_EXPORT bool	v_PostIntegrate (int step)
SOLVER_UTILS_EXPORT void	CheckForRestartTime (NekDouble &time)
Protected Member Functions inherited from Nektar::SolverUtils::EquationSystem
SOLVER_UTILS_EXPORT	EquationSystem (const LibUtilities::SessionReaderSharedPtr &pSession)
	Initialises EquationSystem class members.
int	nocase_cmp (const string &s1, const string &s2)
SOLVER_UTILS_EXPORT void	SetBoundaryConditions (NekDouble time)
	Evaluates the boundary conditions at the given time.
virtual SOLVER_UTILS_EXPORT void	v_TransCoeffToPhys ()
	Virtual function for transformation to physical space.
virtual SOLVER_UTILS_EXPORT void	v_TransPhysToCoeff ()
	Virtual function for transformation to coefficient space.
virtual SOLVER_UTILS_EXPORT void	v_SetInitialConditions (NekDouble initialtime=0.0, bool dumpInitialConditions=true, const int domain=0)
virtual SOLVER_UTILS_EXPORT void	v_EvaluateExactSolution (unsigned int field, Array< OneD, NekDouble > &outfield, const NekDouble time)
SOLVER_UTILS_EXPORT void	SetUpBaseFields (SpatialDomains::MeshGraphSharedPtr &mesh)
SOLVER_UTILS_EXPORT void	ImportFldBase (std::string pInfile, SpatialDomains::MeshGraphSharedPtr pGraph)
virtual SOLVER_UTILS_EXPORT MultiRegions::ExpListSharedPtr	v_GetPressure (void)
virtual SOLVER_UTILS_EXPORT void	v_ExtraFldOutput (std::vector< Array< OneD, NekDouble > > &fieldcoeffs, std::vector< std::string > &variables)

Protected Attributes
Array< OneD, MultiRegions::ExpListSharedPtr >	m_vessels
int	m_nDomains
int	m_currentDomain
int	m_nVariables
UpwindTypePulse	m_upwindTypePulse
Array< OneD, int >	m_fieldPhysOffset
NekDouble	m_rho
NekDouble	m_pext
NekDouble	m_C
NekDouble	m_RT
NekDouble	m_pout
Array< OneD, Array< OneD, NekDouble > >	m_A_0
Array< OneD, Array< OneD, NekDouble > >	m_A_0_trace
Array< OneD, Array< OneD, NekDouble > >	m_beta
Array< OneD, Array< OneD, NekDouble > >	m_beta_trace
Array< OneD, Array< OneD, NekDouble > >	m_trace_fwd_normal
std::vector< std::vector < InterfacePointShPtr > >	m_vesselJcts
std::vector< std::vector < InterfacePointShPtr > >	m_bifurcations
std::vector< std::vector < InterfacePointShPtr > >	m_mergingJcts
Protected Attributes inherited from Nektar::SolverUtils::UnsteadySystem
int	m_infosteps
	Number of time steps between outputting status information.
LibUtilities::TimeIntegrationWrapperSharedPtr	m_intScheme
	Wrapper to the time integration scheme.
LibUtilities::TimeIntegrationSchemeOperators	m_ode
	The time integration scheme operators to use.
LibUtilities::TimeIntegrationSolutionSharedPtr	m_intSoln
NekDouble	m_epsilon
bool	m_explicitDiffusion
	Indicates if explicit or implicit treatment of diffusion is used.
bool	m_explicitAdvection
	Indicates if explicit or implicit treatment of advection is used.
bool	m_explicitReaction
	Indicates if explicit or implicit treatment of reaction is used.
bool	m_homoInitialFwd
	Flag to determine if simulation should start in homogeneous forward transformed state.
std::vector< int >	m_intVariables
std::vector< FilterSharedPtr >	m_filters
Protected Attributes inherited from Nektar::SolverUtils::EquationSystem
LibUtilities::CommSharedPtr	m_comm
	Communicator.
LibUtilities::SessionReaderSharedPtr	m_session
	The session reader.
LibUtilities::FieldIOSharedPtr	m_fld
	Field input/output.
Array< OneD, MultiRegions::ExpListSharedPtr >	m_fields
	Array holding all dependent variables.
Array< OneD, MultiRegions::ExpListSharedPtr >	m_base
	Base fields.
Array< OneD, MultiRegions::ExpListSharedPtr >	m_derivedfields
	Array holding all dependent variables.
SpatialDomains::BoundaryConditionsSharedPtr	m_boundaryConditions
	Pointer to boundary conditions object.
SpatialDomains::MeshGraphSharedPtr	m_graph
	Pointer to graph defining mesh.
std::string	m_filename
	Filename.
std::string	m_sessionName
	Name of the session.
NekDouble	m_time
	Current time of simulation.
NekDouble	m_fintime
	Finish time of the simulation.
NekDouble	m_timestep
	Time step size.
NekDouble	m_lambda
	Lambda constant in real system if one required.
NekDouble	m_checktime
	Time between checkpoints.
int	m_steps
	Number of steps to take.
int	m_checksteps
	Number of steps between checkpoints.
int	m_spacedim
	Spatial dimension (>= expansion dim).
int	m_expdim
	Expansion dimension.
bool	m_SingleMode
	Flag to determine if single homogeneous mode is used.
bool	m_HalfMode
	Flag to determine if half homogeneous mode is used.
bool	m_MultipleModes
	Flag to determine if use multiple homogenenous modes are used.
bool	m_useFFT
	Flag to determine if FFT is used for homogeneous transform.
bool	m_homogen_dealiasing
	Flag to determine if dealiasing is used for homogeneous simulations.
bool	m_specHP_dealiasing
	Flag to determine if dealisising is usde for the Spectral/hp element discretisation.
enum MultiRegions::ProjectionType	m_projectionType
	Type of projection; e.g continuous or discontinuous.
Array< OneD, Array< OneD, NekDouble > >	m_traceNormals
	Array holding trace normals for DG simulations in the forwards direction.
Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_gradtan
	1 x nvariable x nq
Array< OneD, Array< OneD, Array< OneD, NekDouble > > >	m_tanbasis
	2 x m_spacedim x nq
Array< OneD, bool >	m_checkIfSystemSingular
	Flag to indicate if the fields should be checked for singularity.
LibUtilities::FieldMetaDataMap	m_fieldMetaDataMap
	Map to identify relevant solver info to dump in output fields.
int	m_NumQuadPointsError
	Number of Quadrature points used to work out the error.
enum HomogeneousType	m_HomogeneousType
NekDouble	m_LhomX
	physical length in X direction (if homogeneous)
NekDouble	m_LhomY
	physical length in Y direction (if homogeneous)
NekDouble	m_LhomZ
	physical length in Z direction (if homogeneous)
int	m_npointsX
	number of points in X direction (if homogeneous)
int	m_npointsY
	number of points in Y direction (if homogeneous)
int	m_npointsZ
	number of points in Z direction (if homogeneous)
int	m_HomoDirec
	number of homogenous directions
int	m_NumMode
	Mode to use in case of single mode analysis.

Private Member Functions
void	SetUpDomainInterfaces (void)
void	FillDataFromInterfacePoint (InterfacePointShPtr &I, const Array< OneD, const Array< OneD, NekDouble > > &field, NekDouble &A, NekDouble &u, NekDouble &beta, NekDouble &A_0)

Additional Inherited Members
Public Attributes inherited from Nektar::SolverUtils::UnsteadySystem
NekDouble	m_cflSafetyFactor
	CFL safety factor (comprise between 0 to 1).
Protected Types inherited from Nektar::SolverUtils::EquationSystem
enum	HomogeneousType { eHomogeneous1D, eHomogeneous2D, eHomogeneous3D, eNotHomogeneous }
	Parameter for homogeneous expansions. More...

Detailed Description

Base class for unsteady solvers.

Initialises the arterial subdomains in m_vessels and sets up all domain-linking conditions (bifurcations, junctions, merging flows). Detects the network structure and assigns boundary conditons. Also provides the underlying timestepping framework for pulse wave solvers including the general timestepping routines.

Definition at line 86 of file PulseWaveSystem.h.

Constructor & Destructor Documentation

Nektar::PulseWaveSystem::~PulseWaveSystem ( )

virtual

Destructor.

Destructor

Definition at line 72 of file PulseWaveSystem.cpp.

{

}

Nektar::PulseWaveSystem::PulseWaveSystem ( const LibUtilities::SessionReaderSharedPtr & m_session )

protected

Initialises PulseWaveSystem class members.

Processes SolverInfo parameters from the session file and sets up timestepping-specific code.

Parameters

m_Session Session object to read parameters from.

Definition at line 64 of file PulseWaveSystem.cpp.

        : UnsteadySystem(m_session)
    {
    }

Member Function Documentation

void Nektar::PulseWaveSystem::BifurcationRiemann	(	Array< OneD, NekDouble > &	Au,
		Array< OneD, NekDouble > &	uu,
		Array< OneD, NekDouble > &	beta,
		Array< OneD, NekDouble > &	A_0
	)

protected

Riemann Problem for Bifurcation.

Solves the Riemann problem at a bifurcation by assuming subsonic flow at both sides of the boundary and by applying conservation of mass and continuity of the total pressure $\frac{p}{rho} + \frac{u^{2}}{2}.$ The other 3 missing equations come from the characteristic variables. For further information see "Pulse WavePropagation in the human vascular system" Section 3.4.4

Definition at line 652 of file PulseWaveSystem.cpp.

References ASSERTL0, and m_rho.

Referenced by EnforceInterfaceConditions().

    {
            NekDouble rho = m_rho;
            Array<OneD, NekDouble> W(3);
            Array<OneD, NekDouble> W_Au(3);
            Array<OneD, NekDouble> P_Au(3);
            Array<OneD, NekDouble> f(6);
            Array<OneD, NekDouble> g(6);
            Array<OneD, NekDouble> tmp(6);
            Array<OneD, Array<OneD, NekDouble> > inv_J(6);
            for (int i=0; i<6; i++)
            {
                inv_J[i] = Array<OneD, NekDouble> (6);
            }
            NekDouble k = 0.0;
            NekDouble k1 = 0.0;
            NekDouble k2 = 0.0;
            NekDouble k3 = 0.0;
            
            int proceed = 1;
            int iter = 0;
            int MAX_ITER = 7;
            
            // Calculated from input
            W[0] = uu[0] + 4*sqrt(beta[0]/(2*rho))*(sqrt(sqrt(Au[0])) - sqrt(sqrt(A_0[0])));
            W[1] = uu[1] - 4*sqrt(beta[1]/(2*rho))*(sqrt(sqrt(Au[1])) - sqrt(sqrt(A_0[1])));
            W[2] = uu[2] - 4*sqrt(beta[2]/(2*rho))*(sqrt(sqrt(Au[2])) - sqrt(sqrt(A_0[2])));
            // Tolerances for the algorithm
            NekDouble Tol = 1.0e-10;
            
            // Newton Iteration
            while ((proceed) && (iter < MAX_ITER))
            {
                iter = iter+1;
                
                // Calculate the constraint vector, six equations:
                // 3 characteristic variables, mass conservation, 
                // total pressure
                W_Au[0] = 4*sqrt(beta[0]/(2*rho))*(sqrt(sqrt(Au[0])) - sqrt(sqrt(A_0[0])));
                W_Au[1] = 4*sqrt(beta[1]/(2*rho))*(sqrt(sqrt(Au[1])) - sqrt(sqrt(A_0[1])));
                W_Au[2] = 4*sqrt(beta[2]/(2*rho))*(sqrt(sqrt(Au[2])) - sqrt(sqrt(A_0[2])));
                
                P_Au[0] = beta[0]*(sqrt(Au[0]) - sqrt(A_0[0]));
                P_Au[1] = beta[1]*(sqrt(Au[1]) - sqrt(A_0[1]));
                P_Au[2] = beta[2]*(sqrt(Au[2]) - sqrt(A_0[2]));
                
                f[0] = uu[0] + W_Au[0] - W[0];
                f[1] = uu[1] - W_Au[1] - W[1];
                f[2] = uu[2] - W_Au[2] - W[2];
                f[3] = Au[0]*uu[0] - Au[1]*uu[1] - Au[2]*uu[2];
                f[4] = uu[0]*uu[0] + 2.0/rho*P_Au[0] - uu[1]*uu[1] - 2.0/rho*P_Au[1];
                f[5] = uu[0]*uu[0] + 2.0/rho*P_Au[0] - uu[2]*uu[2] - 2.0/rho*P_Au[2];
                    
                    // Calculate the wave speed at each vessel
                    NekDouble c1 = sqrt(beta[0]/(2*rho))*sqrt(sqrt(Au[0]));
                    NekDouble c2 = sqrt(beta[1]/(2*rho))*sqrt(sqrt(Au[1]));
                    NekDouble c3 = sqrt(beta[2]/(2*rho))*sqrt(sqrt(Au[2]));
                    // Inverse Jacobian matrix J(x[n])^(-1), is
                    // already inverted here analytically
                    k = c1*Au[1]*c3+Au[0]*c3*c2+Au[2]*c1*c2;
                    k1 = (c1-uu[0])*k;
                    inv_J[0][0] = (-c2*uu[0]*c3*Au[0]+Au[2]*c2*c1*c1+Au[1]*c1*c1*c3)/k1;
                    inv_J[0][1] = Au[1]*(c2-uu[1])*c1*c3/k1;
                    inv_J[0][2] = Au[2]*(c3-uu[2])*c1*c2/k1;
                    inv_J[0][3] = c1*c2*c3/k1;
                    inv_J[0][4] = -0.5*c1*Au[1]*c3/k1;
                    inv_J[0][5] = -0.5*Au[2]*c1*c2/k1;
                    
                    k2 = (c2+uu[1])*k;
                    inv_J[1][0] = Au[0]*(c1+uu[0])*c2*c3/k2;
                    inv_J[1][1] = (c1*uu[1]*c3*Au[1]+Au[2]*c1*c2*c2+c3*c2*c2*Au[0])/k2;
                    inv_J[1][2] = -Au[2]*(c3-uu[2])*c1*c2/k2;
                    inv_J[1][3] = -c1*c2*c3/k2;
                    inv_J[1][4] = -0.5*(c1*Au[2]+Au[0]*c3)*c2/k2;
                    inv_J[1][5] = 0.5*Au[2]*c1*c2/k2;
                    
                    k3 = (c3+uu[2])*k;
                    inv_J[2][0] = Au[0]*(c1+uu[0])*c2*c3/k3;
                    inv_J[2][1] = -Au[1]*(c2-uu[1])*c1*c3/k3;
                    inv_J[2][2] = (c1*c2*uu[2]*Au[2]+c1*Au[1]*c3*c3+c2*c3*c3*Au[0])/k3;
                    inv_J[2][3] = -c1*c2*c3/k3;
                    inv_J[2][4] = 0.5*c1*Au[1]*c3/k3;
                    inv_J[2][5] = -0.5*(Au[1]*c1+c2*Au[0])*c3/k3;
                    
                    inv_J[3][0] = Au[0]*(Au[0]*c3*c2-uu[0]*c3*Au[1]-uu[0]*c2*Au[2])/k1;
                    inv_J[3][1] = -Au[0]*Au[1]*(c2-uu[1])*c3/k1;
                    inv_J[3][2] = -Au[0]*Au[2]*(c3-uu[2])*c2/k1;
                    inv_J[3][3] = -Au[0]*c3*c2/k1;
                    inv_J[3][4] = 0.5*Au[0]*Au[1]*c3/k1;
                    inv_J[3][5] = 0.5*Au[0]*c2*Au[2]/k1;
                    
                    inv_J[4][0] = Au[0]*Au[1]*(c1+uu[0])*c3/k2;
                    inv_J[4][1] = -Au[1]*(c1*Au[1]*c3+c1*uu[1]*Au[2]+c3*uu[1]*Au[0])/k2;
                    inv_J[4][2] = -Au[2]*Au[1]*(c3-uu[2])*c1/k2;
                    inv_J[4][3] = -c1*Au[1]*c3/k2;
                    inv_J[4][4] = -0.5*Au[1]*(c1*Au[2]+Au[0]*c3)/k2;
                    inv_J[4][5] = 0.5*Au[2]*Au[1]*c1/k2;
                    
                    inv_J[5][0] = Au[0]*Au[2]*(c1+uu[0])*c2/k3;
                    inv_J[5][1] = -Au[2]*Au[1]*(c2-uu[1])*c1/k3;
                    inv_J[5][2] = -Au[2]*(Au[2]*c1*c2+c1*uu[2]*Au[1]+c2*uu[2]*Au[0])/k3;
                    inv_J[5][3] = -Au[2]*c1*c2/k3;
                    inv_J[5][4] = 0.5*Au[2]*Au[1]*c1/k3;
                    inv_J[5][5] = -0.5*Au[2]*(Au[1]*c1+c2*Au[0])/k3;
                    
                    
                    // Solve the system by multiplying the Jacobian with the vector f:
                    // g = (inv_J)*f
                    for (int j=0; j<6; j++)
                    {
                        tmp[j] =0.0;
                        g[j] = 0.0;
                    }
                    
                    for (int j=0; j<6; j++)
                    {
                        for (int i=0; i<6; i++)
                        {
                    tmp[j] = inv_J[j][i]*f[i];
                    g[j] += tmp[j];
                        }
                    }
                    
                    // Update the solution: x_new = x_old - dx
                    uu[0] = uu[0] - g[0];
                    uu[1] = uu[1] - g[1];
                    uu[2] = uu[2] - g[2];
                    Au[0] = Au[0] - g[3];
                    Au[1] = Au[1] - g[4];
                    Au[2] = Au[2] - g[5];
                    
            // Check if the error of the solution is smaller than Tol
                    if ((g[0]*g[0] + g[1]*g[1] + g[2]*g[2] + g[3]*g[3]+ g[4]*g[4] + g[5]*g[5]) < Tol)
                    {
                        proceed = 0;
                    }
                    
                    // Check if solver converges
                    if (iter >= MAX_ITER)
                    {
                        ASSERTL0(false,"Riemann solver for Bifurcation did not converge");
                    }
        }
    }

void Nektar::PulseWaveSystem::CalcCharacteristicVariables ( int omega )

Definition at line 1291 of file PulseWaveSystem.cpp.

References m_beta, m_rho, m_vessels, Vmath::Smul(), Vmath::Vadd(), Vmath::Vmul(), Vmath::Vsqrt(), and Vmath::Vsub().

    {
        int nq = m_vessels[omega]->GetTotPoints();
        Array<OneD, NekDouble> A = m_vessels[omega]->UpdatePhys();
        Array<OneD, NekDouble> u = m_vessels[omega+1]->UpdatePhys();
        Array<OneD, NekDouble> c(nq);
        //Calc 4*c
        Vmath::Vsqrt(nq,A,1,c,1);
        Vmath::Vmul(nq,m_beta[omega],1,c,1,c,1);
        Vmath::Smul(nq,16.0/(2*m_rho),c,1,c,1);
        Vmath::Vsqrt(nq,c,1,c,1);
        // Characteristics
        Vmath::Vadd(nq,u,1,c,1,A,1);
        Vmath::Vsub(nq,u,1,c,1,u,1);
    }

void Nektar::PulseWaveSystem::CheckPoint_Output ( const int n )

protected

Writes the .fld file at the end of the simulation. Similar to the normal v_Output however the Multidomain output has to be prepared.

Definition at line 1098 of file PulseWaveSystem.cpp.

References Nektar::SolverUtils::EquationSystem::m_sessionName, and WriteVessels().

Referenced by v_DoSolve().

    {
        std::stringstream outname;
        outname << m_sessionName << "_" << n << ".chk";
        WriteVessels(outname.str());    
    }

void Nektar::PulseWaveSystem::EnforceInterfaceConditions ( const Array< OneD, const Array< OneD, NekDouble > > & fields )

protected

Definition at line 563 of file PulseWaveSystem.cpp.

References BifurcationRiemann(), FillDataFromInterfacePoint(), JunctionRiemann(), m_bifurcations, m_mergingJcts, m_nVariables, m_vesselJcts, m_vessels, and MergingRiemann().

Referenced by Nektar::PulseWavePropagation::DoOdeRhs().

    {
        int dom, bcpos;
        Array<OneD, NekDouble>  Au(3),uu(3),beta(3),A_0(3);
        
        // Enfore Bifurcations;
        for(int n = 0; n < m_bifurcations.size(); ++n)
        {
            FillDataFromInterfacePoint(m_bifurcations[n][0],fields,
                                       Au[0],uu[0],beta[0],A_0[0]);
            FillDataFromInterfacePoint(m_bifurcations[n][1],fields,
                                       Au[1],uu[1],beta[1],A_0[1]);
            FillDataFromInterfacePoint(m_bifurcations[n][2],fields,
                                       Au[2],uu[2],beta[2],A_0[2]);
            
            // Solve the Riemann problem for a bifurcation
            BifurcationRiemann(Au, uu, beta, A_0);
            // Store the values into the right positions:
            for(int i = 0; i < 3; ++i)
            {
                dom   = m_bifurcations[n][i]->m_domain;
                bcpos = m_bifurcations[n][i]->m_bcPosition;            
                m_vessels[dom*m_nVariables]  ->UpdateBndCondExpansion(bcpos)->UpdatePhys()[0] = Au[i];
                m_vessels[dom*m_nVariables+1]->UpdateBndCondExpansion(bcpos)->UpdatePhys()[0] = uu[i];
            }
        }
        // Enfore Bifurcations;
        for(int n = 0; n < m_mergingJcts.size(); ++n)
        {
            // Merged vessel
            FillDataFromInterfacePoint(m_mergingJcts[n][0],fields,
                                       Au[0],uu[0],beta[0],A_0[0]);
            FillDataFromInterfacePoint(m_mergingJcts[n][1],fields,
                                       Au[1],uu[1],beta[1],A_0[1]);
            FillDataFromInterfacePoint(m_mergingJcts[n][2],fields,
                                       Au[2],uu[2],beta[2],A_0[2]);
            
            // Solve the Riemann problem for a merging vessel
            MergingRiemann(Au, uu, beta, A_0);
            // Store the values into the right positions:
            for(int i = 0; i < 3; ++i)
            {
                int dom   = m_mergingJcts[n][i]->m_domain;
                int bcpos = m_mergingJcts[n][i]->m_bcPosition;            
                m_vessels[dom*m_nVariables]  ->UpdateBndCondExpansion(bcpos)->UpdatePhys()[0] = Au[i];
                m_vessels[dom*m_nVariables+1]->UpdateBndCondExpansion(bcpos)->UpdatePhys()[0] = uu[i];
            }
        }
        for(int n = 0; n < m_vesselJcts.size(); ++n)
        {
            
            FillDataFromInterfacePoint(m_vesselJcts[n][0],fields,
                                       Au[0],uu[0],beta[0],A_0[0]);
            FillDataFromInterfacePoint(m_vesselJcts[n][1],fields,
                                       Au[1],uu[1],beta[1],A_0[1]);
            
            JunctionRiemann(Au, uu, beta, A_0);
            // Store the values into the right positions:
            for(int i = 0; i < 2; ++i)
            {
                int dom   = m_vesselJcts[n][i]->m_domain;
                int bcpos = m_vesselJcts[n][i]->m_bcPosition;            
                m_vessels[dom*m_nVariables]  ->UpdateBndCondExpansion(bcpos)->UpdatePhys()[0] = Au[i];
                m_vessels[dom*m_nVariables+1]->UpdateBndCondExpansion(bcpos)->UpdatePhys()[0] = uu[i];
                //cout<<"Au: "<<Au[i]<<endl;
                //cout<<"uu: "<<uu[i]<<endl;
                //cout<<endl;
            }
        }
    }

void Nektar::PulseWaveSystem::FillDataFromInterfacePoint	(	InterfacePointShPtr &	I,
		const Array< OneD, const Array< OneD, NekDouble > > &	field,
		NekDouble &	A,
		NekDouble &	u,
		NekDouble &	beta,
		NekDouble &	A_0
	)

private

Definition at line 537 of file PulseWaveSystem.cpp.

References m_A_0_trace, m_beta_trace, m_fieldPhysOffset, m_nVariables, and m_vessels.

Referenced by EnforceInterfaceConditions().

    {
        int omega, traceId, eid, vert, phys_offset, vesselID;
        // Parent vessel
        omega    = I->m_domain;
        traceId  = I->m_traceId;
        eid      = I->m_elmt;
        vert     = I->m_elmtVert;
        vesselID = omega*m_nVariables;
                    
        phys_offset = m_vessels[vesselID]->GetPhys_Offset(eid);
        
        m_vessels[vesselID]->GetExp(eid)->
            GetVertexPhysVals(vert, fields[0]+m_fieldPhysOffset[omega]+phys_offset, A);
        m_vessels[vesselID]->GetExp(eid)->
            GetVertexPhysVals(vert, fields[1]+m_fieldPhysOffset[omega]+phys_offset, u);
        
        beta = m_beta_trace[omega][traceId];
        A_0  = m_A_0_trace [omega][traceId];
    }

int Nektar::PulseWaveSystem::GetNdomains ( )

inline

Definition at line 92 of file PulseWaveSystem.h.

        {
            return m_nDomains;
        }

void Nektar::PulseWaveSystem::JunctionRiemann	(	Array< OneD, NekDouble > &	Au,
		Array< OneD, NekDouble > &	uu,
		Array< OneD, NekDouble > &	beta,
		Array< OneD, NekDouble > &	A_0
	)

protected

Riemann Problem for Junction.

Solves the Riemann problem at an interdomain junction by assuming subsonic flow at both sides of the boundary and by applying conservation of mass and continuity of the total pressure $\frac{p}{rho} + \frac{u^{2}}{2}.$ The other 2 missing equations come from the characteristic variables. For further information see "Pulse WavePropagation in the human vascular system" Section 3.4.

Definition at line 968 of file PulseWaveSystem.cpp.

References ASSERTL0, and m_rho.

Referenced by EnforceInterfaceConditions().

    {       
        NekDouble rho = m_rho;
        Array<OneD, NekDouble> W(2);
        Array<OneD, NekDouble> W_Au(2);
        Array<OneD, NekDouble> P_Au(2);
        Array<OneD, NekDouble> f(4);
        Array<OneD, NekDouble> g(4);
        Array<OneD, NekDouble> tmp(4);
        Array<OneD, Array<OneD, NekDouble> > inv_J(4);
        for (int i=0; i<4; i++)
        {
            inv_J[i] = Array<OneD, NekDouble> (4);
        }
        NekDouble k = 0.0;
        NekDouble k1 = 0.0;
        NekDouble k2 = 0.0;
    
        int proceed = 1;
        int iter = 0;
        int MAX_ITER = 7;
        NekDouble Tol = 1.0e-10;
        
        // Calculated from input
        W[0] = uu[0] + 4*sqrt(beta[0]/(2*rho))*(sqrt(sqrt(Au[0])) - sqrt(sqrt(A_0[0])));
        W[1] = uu[1] - 4*sqrt(beta[1]/(2*rho))*(sqrt(sqrt(Au[1])) - sqrt(sqrt(A_0[1])));
        
        while((proceed) && (iter < MAX_ITER))
        {
            iter = iter+1;
            
            // Calculate the constraint vector, 4 equations:
            // 2 characteristic variables, mass conservation, 
            // total pressure
            W_Au[0] = 4*sqrt(beta[0]/(2*rho))*(sqrt(sqrt(Au[0])) - sqrt(sqrt(A_0[0])));
            W_Au[1] = 4*sqrt(beta[1]/(2*rho))*(sqrt(sqrt(Au[1])) - sqrt(sqrt(A_0[1])));
            
            P_Au[0] = beta[0]*(sqrt(Au[0]) - sqrt(A_0[0]));
            P_Au[1] = beta[1]*(sqrt(Au[1]) - sqrt(A_0[1]));
            
            f[0] = uu[0] + W_Au[0] - W[0];
            f[1] = uu[1] - W_Au[1] - W[1];
            f[2] = Au[0]*uu[0] - Au[1]*uu[1];
            f[3] = uu[0]*uu[0] + 2.0/rho*P_Au[0] - uu[1]*uu[1] - 2.0/rho*P_Au[1];
            
            // Calculate the wave speed at each vessel
            NekDouble cl = sqrt(beta[0]/(2*rho))*sqrt(sqrt(Au[0]));
            NekDouble cr = sqrt(beta[1]/(2*rho))*sqrt(sqrt(Au[1]));
            
            // Inverse Jacobian matrix J(x[n])^(-1), is already inverted here analytically
            k = (cl*Au[1]+Au[0]*cr);
            k1 = (cl-uu[0])*k;
            inv_J[0][0] = (Au[1]*cl*cl-cr*uu[0]*Au[0])/k1;
            inv_J[0][1] = Au[1]*(cr-uu[1])*cl/k1;
            inv_J[0][2] = cl*cr/k1;
            inv_J[0][3] = -0.5*cl*Au[1]/k1;
            
            k2 = (cr+uu[1])*k;
            inv_J[1][0] = Au[0]*(cl+uu[0])*cr/k2;
            inv_J[1][1] = (cl*uu[1]*Au[1]+cr*cr*Au[0])/k2;
            inv_J[1][2] = -cl*cr/k2;
            inv_J[1][3] = -0.5*Au[0]*cr/k2;
            
            inv_J[2][0] = Au[0]*(Au[0]*cr-uu[0]*Au[1])/k1;
            inv_J[2][1] = -Au[0]*Au[1]*(cr-uu[1])/k1;
            inv_J[2][2] = -Au[0]*cr/k1;
            inv_J[2][3] = 0.5*Au[1]*Au[0]/k1;
            
            inv_J[3][0] = Au[0]*Au[1]*(cl+uu[0])/k2;
            inv_J[3][1] = -Au[1]*(cl*Au[1]+uu[1]*Au[0])/k2;
            inv_J[3][2] = -cl*Au[1]/k2;
            inv_J[3][3] = -0.5*Au[1]*Au[0]/k2;
            
            // Solve the system by multiplying the Jacobian with the vector f:
            // g = (inv_J)*f
            for (int j=0; j<4; j++)
            {
                tmp[j] =0.0;
                g[j] = 0.0;
            }
            
            for (int j=0; j<4; j++)
            {
                for (int i=0; i<4; i++)
                {
                    tmp[j] = inv_J[j][i]*f[i];
                    g[j] += tmp[j];
                }
            }
            
            // Update solution: x_new = x_old - dx
            uu[0] -= g[0];
            uu[1] -= g[1];
            Au[0] -= g[2];
            Au[1] -= g[3];
            
            // Check if the error of the solution is smaller than Tol.
            if((g[0]*g[0] + g[1]*g[1] + g[2]*g[2] + g[3]*g[3]) < Tol)      
                proceed = 0;
        }
    
        if(iter >= MAX_ITER)
        {
            ASSERTL0(false,"Riemann solver for Junction did not converge");
        }
    }

void Nektar::PulseWaveSystem::LinkSubdomains ( Array< OneD, Array< OneD, Array< OneD, NekDouble > > > & fields )

protected

Links the subdomains.

void Nektar::PulseWaveSystem::MergingRiemann	(	Array< OneD, NekDouble > &	Au,
		Array< OneD, NekDouble > &	uu,
		Array< OneD, NekDouble > &	beta,
		Array< OneD, NekDouble > &	A_0
	)

protected

Riemann Problem for Merging Flow.

Solves the Riemann problem at an merging flow condition by assuming subsonic flow at both sides of the boundary and by applying conservation of mass and continuity of the total pressure $\frac{p}{rho} + \frac{u^{2}}{2}.$ The other 3 missing equations come from the characteristic variables. For further information see "Pulse WavePropagation in the human vascular system" Section 3.4.4

Definition at line 811 of file PulseWaveSystem.cpp.

References ASSERTL0, and m_rho.

Referenced by EnforceInterfaceConditions().

    {
        NekDouble rho = m_rho;
        Array<OneD, NekDouble> W(3);
        Array<OneD, NekDouble> W_Au(3);
        Array<OneD, NekDouble> P_Au(3);
        Array<OneD, NekDouble> f(6);
        Array<OneD, NekDouble> g(6);
        Array<OneD, NekDouble> tmp(6);
        Array<OneD, Array<OneD, NekDouble> > inv_J(6);
        for (int i=0; i<6; i++)
        {
            inv_J[i] = Array<OneD, NekDouble> (6);
        }
        
        NekDouble k = 0.0;
        NekDouble k1 = 0.0;
        NekDouble k2 = 0.0;
        NekDouble k3 = 0.0;
    
        int proceed = 1;
        int iter = 0;
        int MAX_ITER = 7;
        
        // Calculated from input
        W[0] = uu[0] - 4*sqrt(beta[0]/(2*rho))*(sqrt(sqrt(Au[0])) - sqrt(sqrt(A_0[0])));
        W[1] = uu[1] + 4*sqrt(beta[1]/(2*rho))*(sqrt(sqrt(Au[1])) - sqrt(sqrt(A_0[1])));
        W[2] = uu[2] + 4*sqrt(beta[2]/(2*rho))*(sqrt(sqrt(Au[2])) - sqrt(sqrt(A_0[2])));
        
        // Tolerances for the algorithm
        NekDouble Tol = 1.0e-10;
    
        // Newton Iteration
        while ((proceed) && (iter < MAX_ITER))
        {
            iter = iter+1;
            
            // Calculate the constraint vector, six equations:
            // 3 characteristic variables, mass conservation, 
            // total pressure
            W_Au[0] = 4*sqrt(beta[0]/(2*rho))*(sqrt(sqrt(Au[0])) - sqrt(sqrt(A_0[0])));
            W_Au[1] = 4*sqrt(beta[1]/(2*rho))*(sqrt(sqrt(Au[1])) - sqrt(sqrt(A_0[1])));
            W_Au[2] = 4*sqrt(beta[2]/(2*rho))*(sqrt(sqrt(Au[2])) - sqrt(sqrt(A_0[2])));
            
            P_Au[0] = beta[0]*(sqrt(Au[0]) - sqrt(A_0[0]));
            P_Au[1] = beta[1]*(sqrt(Au[1]) - sqrt(A_0[1]));
            P_Au[2] = beta[2]*(sqrt(Au[2]) - sqrt(A_0[2]));
            
            f[0] = uu[0] - W_Au[0] - W[0];
            f[1] = uu[1] + W_Au[1] - W[1];
            f[2] = uu[2] + W_Au[2] - W[2];
            f[3] = Au[0]*uu[0] - Au[1]*uu[1] - Au[2]*uu[2];
            f[4] = uu[0]*uu[0] + 2.0/rho*P_Au[0] - uu[1]*uu[1] - 2.0/rho*P_Au[1];
            f[5] = uu[0]*uu[0] + 2.0/rho*P_Au[0] - uu[2]*uu[2] - 2.0/rho*P_Au[2];
            
            // Calculate the wave speed at each vessel
            NekDouble c1 = sqrt(beta[0]/(2*rho))*sqrt(sqrt(Au[0]));
            NekDouble c2 = sqrt(beta[1]/(2*rho))*sqrt(sqrt(Au[1]));
            NekDouble c3 = sqrt(beta[2]/(2*rho))*sqrt(sqrt(Au[2]));
            
            // Inverse Jacobian matrix J(x[n])^(-1), is already inverted here analytically
            k = c1*Au[1]*c3+Au[0]*c3*c2+Au[2]*c1*c2;
            k1 = (c1+uu[0])*k;
            inv_J[0][0] = (c2*uu[0]*c3*Au[0]+Au[2]*c2*c1*c1+Au[1]*c1*c1*c3)/k1;
            inv_J[0][1] = Au[1]*(c2+uu[1])*c1*c3/k1;
            inv_J[0][2] = Au[2]*(c3+uu[2])*c1*c2/k1;
            inv_J[0][3] = c1*c2*c3/k1;
            inv_J[0][4] = 0.5*Au[1]*c1*c3/k1;
            inv_J[0][5] = 0.5*Au[2]*c1*c2/k1;
            
            k2 = (c2-uu[1])*k;
            inv_J[1][0] = Au[0]*(c1-uu[0])*c2*c3/k2;
            inv_J[1][1] = (-c1*uu[1]*c3*Au[1]+Au[2]*c1*c2*c2+c3*c2*c2*Au[0])/k2;
            inv_J[1][2] = -Au[2]*(c3+uu[2])*c1*c2/k2;
            inv_J[1][3] = -c1*c2*c3/k2;
            inv_J[1][4] = 0.5*(c1*Au[2]+Au[0]*c3)*c2/k2;
            inv_J[1][5] = -0.5*Au[2]*c1*c2/k2;
            
            k3 = (c3-uu[2])*k;
            inv_J[2][0] = Au[0]*(c1-uu[0])*c2*c3/k3;
            inv_J[2][1] = -Au[1]*(c2+uu[1])*c1*c3/k3;
            inv_J[2][2] = -(c1*uu[2]*c2*Au[2]-Au[1]*c1*c3*c3-c2*c3*c3*Au[0])/k3;
            inv_J[2][3] = -c1*c2*c3/k3;
            inv_J[2][4] = -0.5*Au[1]*c1*c3/k3;
            inv_J[2][5] = 0.5*(Au[1]*c1+Au[0]*c2)*c3/k3;
            
            inv_J[3][0] = -Au[0]*(Au[0]*c3*c2+uu[0]*c3*Au[1]+uu[0]*c2*Au[2])/k1;
            inv_J[3][1] = Au[0]*Au[1]*(c2+uu[1])*c3/k1;
            inv_J[3][2] = Au[0]*Au[2]*(c3+uu[2])*c2/k1;
            inv_J[3][3] = Au[0]*c3*c2/k1;
            inv_J[3][4] = 0.5*Au[0]*Au[1]*c3/k1;
            inv_J[3][5] = 0.5*Au[0]*c2*Au[2]/k1;
            
            inv_J[4][0] = -Au[0]*Au[1]*(c1-uu[0])*c3/k2;
            inv_J[4][1] = Au[1]*(Au[1]*c1*c3-c1*uu[1]*Au[2]-c3*uu[1]*Au[0])/k2;
            inv_J[4][2] = Au[2]*Au[1]*(c3+uu[2])*c1/k2;
            inv_J[4][3] = Au[1]*c1*c3/k2;
            inv_J[4][4] = -0.5*Au[1]*(c1*Au[2]+Au[0]*c3)/k2;
            inv_J[4][5] = 0.5*Au[2]*Au[1]*c1/k2;
            
            inv_J[5][0] = -Au[0]*Au[2]*(c1-uu[0])*c2/k3;
            inv_J[5][1] = Au[2]*Au[1]*(c2+uu[1])*c1/k3;
            inv_J[5][2] = Au[2]*(Au[2]*c1*c2-c1*uu[2]*Au[1]-c2*uu[2]*Au[0])/k3;
            inv_J[5][3] = Au[2]*c1*c2/k3;
            inv_J[5][4] = 0.5*Au[2]*Au[1]*c1/k3;
            inv_J[5][5] = -0.5*Au[2]*(Au[1]*c1+Au[0]*c2)/k3;
            
            // Solve the system by multiplying the Jacobian with the vector f:
            // g = (inv_J)*f
            for (int j=0; j<6; j++)
            {
                tmp[j] =0.0;
                g[j] = 0.0;
            }
            
            for (int j=0; j<6; j++)
            {
                for (int i=0; i<6; i++)
                {
                    tmp[j] = inv_J[j][i]*f[i];
                    g[j] += tmp[j];
                }
            }
            
            // Update the solution: x_new = x_old - dx
            uu[0] = uu[0] - g[0];
            uu[1] = uu[1] - g[1];
            uu[2] = uu[2] - g[2];
            Au[0] = Au[0] - g[3];
            Au[1] = Au[1] - g[4];
            Au[2] = Au[2] - g[5];
            
            // Check if the error of the solution is smaller than Tol
            if ((g[0]*g[0] + g[1]*g[1] + g[2]*g[2] + g[3]*g[3]+ g[4]*g[4] + g[5]*g[5]) < Tol)
            {
                proceed = 0;
            }
            
            // Check if solver converges
            if (iter >= MAX_ITER)
            {
                ASSERTL0(false,"Riemann solver for Merging Flow did not converge");
            }
            
        }
    }

void Nektar::PulseWaveSystem::SetUpDomainInterfaces ( void )

private

Definition at line 262 of file PulseWaveSystem.cpp.

References ASSERTL0, Nektar::SpatialDomains::eDirichlet, Nektar::SpatialDomains::eNotDefined, ErrorUtil::ewarning, Nektar::iterator, m_bifurcations, m_mergingJcts, m_nDomains, m_nVariables, m_vesselJcts, m_vessels, and NEKERROR.

Referenced by v_InitObject().

    {
        map<int,std::vector<InterfacePointShPtr> > VidToDomain;
        map<int,std::vector<InterfacePointShPtr> >::iterator iter;
        // loop over domain and find out if we have any undefined
        // boundary conditions representing interfaces. If so make a
        // map based around vid and storing the domains that are
        // part of interfaces. 
        for(int omega = 0; omega < m_nDomains; ++omega)
        {
            int vesselID = omega*m_nVariables;
            
            for(int i = 0; i < 2; ++i)
            {
                if(m_vessels[vesselID]->GetBndConditions()[i]->GetBoundaryConditionType() == SpatialDomains::eNotDefined)
                {                    
                    // Get Vid of interface
                    int vid  = m_vessels[vesselID]->UpdateBndCondExpansion(i)->GetExp(0)->GetGeom()->GetVid(0);
                    cout<<"Shared vertex id: "<<vid<<endl;
                    MultiRegions::ExpListSharedPtr trace = m_vessels[vesselID]->GetTrace(); 
                    InterfacePointShPtr Ipt; 
                    bool finish = false;
                    // find which elmt, the lcoal vertex and the data offset of point
                    for(int n = 0; n < m_vessels[vesselID]->GetExpSize(); ++n)
                    {
                        for(int p = 0; p < 2; ++p)
                        {
                            if(m_vessels[vesselID]->GetTraceMap()->GetElmtToTrace()[n][p]->as<LocalRegions::Expansion>()->GetGeom()->GetVid(0) == vid)
                            {
                                int eid = m_vessels[vesselID]->GetTraceMap()->GetElmtToTrace()[n][p]->GetElmtId();
                                int tid = m_vessels[vesselID]->GetTrace()->GetCoeff_Offset(eid);
                                Ipt = MemoryManager<InterfacePoint>::AllocateSharedPtr(vid,omega,n,p,tid,i);
                                cout<<"Global Vid of interface point: "<<vid<<endl;
                                cout<<"Domain interface point belongs to: "<<omega<<endl;
                                cout<<"Element id of vertex: "<<n<<endl;
                                cout<<"Vertex id within local element: "<<p<<endl; 
                                cout<<"Element id  within the trace: "<<tid<<endl; 
                                cout<<"Position of boundary condition in region: "<<i<<endl;
                                finish = true;
                                break;
                            }
                        }
                        if(finish == true)
                        {
                            break;
                        }
                    }
                    
                    VidToDomain[vid].push_back(Ipt);
                    
                    // finally reset boundary condition to Dirichlet
                    m_vessels[vesselID]->GetBndConditions()[i]
                        ->SetBoundaryConditionType(SpatialDomains::eDirichlet);
                    
                    m_vessels[vesselID+1]->GetBndConditions()[i]
                        ->SetBoundaryConditionType(SpatialDomains::eDirichlet);
                }
            }
        }
        // loop over map and set up Interface information;
        for(iter = VidToDomain.begin(); iter != VidToDomain.end(); ++iter)
        {
            if(iter->second.size() == 2) // Vessel jump interface
            {
                m_vesselJcts.push_back(iter->second);
            }
            else if(iter->second.size() == 3) // Bifurcation or Merging junction. 
            {
                int nbeg = 0;
                int nend = 0;
                // Determine if bifurcation or merging junction
                // through number of elemnt vertices that meet at
                // junction. Only one vertex using a m_elmtVert=1
                // indicates a bifurcation
                for(int i = 0; i < 3; ++i)
                {
                    if(iter->second[i]->m_elmtVert == 0)
                    {
                        nbeg += 1;
                    }
                    else
                    {
                        nend += 1;
                    }
                }
                // Set up Bifurcation information 
                if(nbeg == 2)
                {
                    // ensure first InterfacePoint is parent 
                    if(iter->second[0]->m_elmtVert == 1) //m_elmtVert: Vertex id in local element
                    {
                        m_bifurcations.push_back(iter->second);
                    }
                    else
                    {
                        //order points according to Riemann solver convention
                        InterfacePointShPtr I;
                        //find merging vessel 
                        if(iter->second[1]->m_elmtVert == 1)
                        {
                            I = iter->second[0];
                            iter->second[0] = iter->second[1];
                            iter->second[1] = I;
                        }
                        else if (iter->second[2]->m_elmtVert == 1)
                        {
                            I = iter->second[0];
                            iter->second[0] = iter->second[2];
                            iter->second[2] = I;
                        }
                        NEKERROR(ErrorUtil::ewarning,"This routine has not been checked");
                    }                    
                }
                else
                {
                    // ensure last InterfacePoint is merged vessel
                    if(iter->second[0]->m_elmtVert == 0)
                    {
                        m_mergingJcts.push_back(iter->second);
                    }
                    else
                    {
                        //order points according to Riemann solver convention
                        InterfacePointShPtr I;
                        //find merging vessel 
                        if(iter->second[1]->m_elmtVert == 0)
                        {
                            I = iter->second[0];
                            iter->second[0] = iter->second[1];
                            iter->second[1] = I;
                        }
                        else if (iter->second[2]->m_elmtVert == 0)
                        {
                            I = iter->second[0];
                            iter->second[0] = iter->second[2];
                            iter->second[2] = I;
                        }
                        NEKERROR(ErrorUtil::ewarning,"This routine has not been checked");
                    }
                }
                
            }
            else
            {
                ASSERTL0(false,"Unknown junction type");
            }
        }
    }

Array<OneD, MultiRegions::ExpListSharedPtr> Nektar::PulseWaveSystem::UpdateVessels ( void )

inline

Definition at line 97 of file PulseWaveSystem.h.

        {
            return m_vessels;
        }

void Nektar::PulseWaveSystem::v_DoInitialise ( void )

protectedvirtual

Sets up initial conditions.

Initialisation routine for multiple subdomain case. Sets the initial conditions for all arterial subdomains read from the inputfile. Sets the material properties and the A_0 area for all subdomains and fills the domain-linking boundary conditions with the initial values of their domain.

Reimplemented from Nektar::SolverUtils::UnsteadySystem.

Definition at line 427 of file PulseWaveSystem.cpp.

References Nektar::SolverUtils::EquationSystem::m_fields, m_nDomains, m_nVariables, Nektar::SolverUtils::EquationSystem::m_session, m_vessels, and Nektar::SolverUtils::EquationSystem::SetInitialConditions().

    {
        
        if (m_session->GetComm()->GetRank() == 0)
        {
            cout << "Initial Conditions:" << endl;
        }
    
        /* Loop over all subdomains to initialize all with the Initial
         * Conditions read from the inputfile*/
        for (int omega = 0; omega < m_nDomains; omega++)
        {
            m_fields[0] = m_vessels[m_nVariables*omega];
            m_fields[1] = m_vessels[m_nVariables*omega+1];
            
            if (m_session->GetComm()->GetRank() == 0)
            {
                cout << "Subdomain = " <<omega<<endl;
            }
            
            SetInitialConditions(0.0,0,omega);
        }   
        // Reset to first definition
        m_fields[0] = m_vessels[0];
        m_fields[1] = m_vessels[1];
            
    }

void Nektar::PulseWaveSystem::v_DoSolve ( void )

protectedvirtual

Solves an unsteady problem.

NEEDS Updating:

DoSolve routine for PulseWavePropagation with multiple subdomains taken from UnsteadySystem and modified for multidomain case. Initialises the time integration scheme (as specified in the session file), and perform the time integration. Within the timestepping loop the following is done: 1. Link all arterial segments according to the network structure, solve the Riemann problem between different arterial segments and assign the values to the boundary conditions (LinkSubdomains) 2. Every arterial segment is solved independentl for this timestep. This is done by handing the solution vector $\mathbf{u}$ and the right hand side m_ode, which is the PulseWavePropagation class in this example over to the time integration scheme

Reimplemented from Nektar::SolverUtils::UnsteadySystem.

Definition at line 472 of file PulseWaveSystem.cpp.

    {
        NekDouble IntegrationTime = 0.0;
        int i,n,nchk = 1;
    
        Array<OneD, Array<OneD,NekDouble> >  fields(m_nVariables);          
    
        for(int i = 0; i < m_nVariables; ++i)
        {
            fields[i]  = m_vessels[i]->UpdatePhys();
            m_fields[i]->SetPhysState(false);
        }
        
        m_intSoln = m_intScheme->InitializeScheme(
                m_timestep,fields,m_time,m_ode);
        // Time loop
        for(n = 0; n < m_steps; ++n)
        {               
            Timer timer;
            timer.Start();
            fields = m_intScheme->TimeIntegrate(n,m_timestep,m_intSoln,m_ode);
            //cout<<"integration: "<<fields[0][fields[0].num_elements()-1]<<endl;                
            m_time += m_timestep;
            timer.Stop();
            IntegrationTime += timer.TimePerTest(1);
            
            // Write out status information.
            if(m_session->GetComm()->GetRank() == 0 && !((n+1)%m_infosteps))
            {
                cout << "Steps: " << n+1
                     << "\t Time: " << m_time
                     << "\t Time-step: " << m_timestep << "\t" << endl;
            }
            
            // Transform data if needed
            if(!((n+1)%m_checksteps))
            {
                for (i = 0; i < m_nVariables; ++i)
                {
                    int cnt = 0;
                    for (int omega = 0; omega < m_nDomains; omega++)
                    {
                        m_vessels[omega*m_nVariables+i]->FwdTrans(fields[i]+cnt,
                                     m_vessels[omega*m_nVariables+i]->UpdateCoeffs());
                        cnt += m_vessels[omega*m_nVariables+i]->GetTotPoints();
                    }
                }
                CheckPoint_Output(nchk++);
            }
            
        }//end of timeintegration
    
        //Copy Array To Vessel Phys Fields
        for(int i = 0; i < m_nVariables; ++i)
        {
            Vmath::Vcopy(fields[i].num_elements(), fields[i],1,m_vessels[i]->UpdatePhys(),1);
        }
        
        cout <<"Time-integration timing : " 
             << IntegrationTime << " s" << endl << endl;
    }   

void Nektar::PulseWaveSystem::v_InitObject ( )

protectedvirtual

Initialisation routine for multidomain solver. Sets up the expansions for every arterial segment (m_vessels) and for one complete field m_outfield which is needed to write the postprocessing output. Also determines which upwind strategy is used (currently only upwinding scheme available) and reads blodd flow specific parameters from the inputfile

Gets the Material Properties of each arterial segment
specified in the inputfile from section MaterialProperties

Also gets the Area at static equilibrium A_0 specified in the inputfile.

Having found these points also extract the values at the trace points and the normal direction consistent with the left adjacent definition of Fwd and Bwd

Reimplemented from Nektar::SolverUtils::UnsteadySystem.

Reimplemented in Nektar::PulseWavePropagation, and Nektar::PulseWaveSystemOutput.

Definition at line 85 of file PulseWaveSystem.cpp.

    {
        // Initialise base class
        UnsteadySystem::v_InitObject();
        // Read the geometry and the expansion information
        m_nDomains = m_graph->GetDomain().size();
        
        // Determine projectiontype
        ASSERTL0(m_session->MatchSolverInfo("Projection","DisContinuous"),"Pulse solver only set up for Discontinuous projections");
        m_projectionType = MultiRegions::eDiscontinuous;
        ASSERTL0(m_graph->GetMeshDimension() == 1,"Pulse wave solver only set up for expansion dimension equal to 1");
        
        int i;
        m_nVariables =  m_session->GetVariables().size();
    
        m_fields  = Array<OneD, MultiRegions::ExpListSharedPtr> (m_nVariables);
        m_vessels = Array<OneD, MultiRegions::ExpListSharedPtr> (m_nVariables*m_nDomains);
        const std::vector<SpatialDomains::CompositeMap> domain = m_graph->GetDomain();
            
        SpatialDomains::BoundaryConditions Allbcs(m_session, m_graph);
        // Set up domains and put geometry to be only one space dimension. 
        int cnt = 0;
        bool SetToOneSpaceDimension = true;
        if(m_session->DefinesCmdLineArgument("SetToOneSpaceDimension"))
        {
            std::string cmdline = m_session->GetCmdLineArgument<std::string>("SetToOneSpaceDimension");
            if(boost::to_upper_copy(cmdline) == "FALSE")
            {
                SetToOneSpaceDimension  = false;
            }
        }
        for(i = 0 ; i < m_nDomains; ++i)
        {
            for(int j = 0; j < m_nVariables; ++j)
            {
                m_vessels[cnt++] = MemoryManager<MultiRegions::DisContField1D>
                    ::AllocateSharedPtr(m_session, m_graph, domain[i],
                                        Allbcs,
                                        m_session->GetVariable(j),
                                        SetToOneSpaceDimension);
            }
        }
        // Reset coeff and phys space to be continuous over all domains
        int totcoeffs = 0;
        int totphys   = 0;
        m_fieldPhysOffset = Array<OneD, int>(m_nDomains+1,0);
        for(i = 0; i < m_nDomains; ++i)
        {
            totcoeffs += m_vessels[i*m_nVariables]->GetNcoeffs();
            m_fieldPhysOffset[i] = totphys;
            totphys   += m_vessels[i*m_nVariables]->GetTotPoints();
        }
        m_fieldPhysOffset[m_nDomains] = totphys;
        for(int n = 0; n < m_nVariables; ++n)
        {
            Array<OneD, NekDouble> coeffs(totcoeffs,0.0);
            Array<OneD, NekDouble> phys(totphys,0.0);
            Array<OneD, NekDouble> tmpcoeffs,tmpphys;
            m_vessels[n]->SetCoeffsArray(coeffs);
            m_vessels[n]->SetPhysArray(phys);
            int cnt  = m_vessels[n]->GetNcoeffs();
            int cnt1 = m_vessels[n]->GetTotPoints();
            for(i = 1; i < m_nDomains; ++i)
            {
                m_vessels[i*m_nVariables+n]->SetCoeffsArray(tmpcoeffs = coeffs + cnt);
                m_vessels[i*m_nVariables+n]->SetPhysArray   (tmpphys = phys + cnt1);
                cnt  += m_vessels[i*m_nVariables+n]->GetNcoeffs();
                cnt1 += m_vessels[i*m_nVariables+n]->GetTotPoints();                
            }
        }
        
        // Set Default Parameter
        m_session->LoadParameter("Time",     m_time, 0.0);
        m_session->LoadParameter("TimeStep", m_timestep, 0.01);
        m_session->LoadParameter("NumSteps", m_steps, 0);
        m_session->LoadParameter("IO_CheckSteps", m_checksteps, m_steps);
        m_session->LoadParameter("FinTime", m_fintime, 0);
        m_session->LoadParameter("NumQuadPointsError", m_NumQuadPointsError, 0);
        
        m_fields[0] = m_vessels[0];
        m_fields[1] = m_vessels[1];
    
        // Zero all physical fields initially.
        ZeroPhysFields();
        
        // If Discontinuous Galerkin determine upwinding method to use
        for (int i = 0; i < (int)SIZE_UpwindTypePulse; ++i)
        {
            bool match;
            m_session->MatchSolverInfo("UPWINDTYPEPULSE", UpwindTypeMapPulse[i], match, false);
            if (match)
            {
                m_upwindTypePulse = (UpwindTypePulse) i;
                break;
            }
        }
        // Load solver- specific parameters
        m_session->LoadParameter("IO_InfoSteps", m_infosteps, 0);
        // Load blood density
        m_session->LoadParameter("rho", m_rho, 0.5);
        // Load external pressure
        m_session->LoadParameter("pext", m_pext, 0.0);
        
        int nq = 0;
        /**
         *  Gets the Material Properties of each arterial segment
         *  specified in the inputfile from section MaterialProperties
     *  Also gets the Area at static equilibrium A_0 specified in the
     *  inputfile. 
         *
         * Having found these points also extract the values at the
         * trace points and the normal direction consistent with the
         * left adjacent definition of Fwd and Bwd
     */
        m_beta       = Array<OneD, Array<OneD, NekDouble> >(m_nDomains);
        m_beta_trace = Array<OneD, Array<OneD, NekDouble> >(m_nDomains);
        m_A_0        = Array<OneD, Array<OneD, NekDouble> >(m_nDomains);
        m_A_0_trace  = Array<OneD, Array<OneD, NekDouble> >(m_nDomains);
        m_trace_fwd_normal = Array<OneD, Array<OneD, NekDouble> >(m_nDomains);
        
        for (int omega = 0; omega < m_nDomains; omega++)
        {
            nq = m_vessels[2*omega]->GetNpoints();
            m_fields[0] = m_vessels[2*omega];
            
            m_beta[omega] = Array<OneD, NekDouble>(nq);
            EvaluateFunction("beta", m_beta[omega],"MaterialProperties",0.0,omega);
            m_A_0[omega] = Array<OneD, NekDouble>(nq); 
            EvaluateFunction("A_0", m_A_0[omega],"A_0",0.0,omega);
            int nqTrace = GetTraceTotPoints();
            m_beta_trace[omega] = Array<OneD, NekDouble>(nqTrace);
            m_fields[0]->ExtractTracePhys(m_beta[omega],m_beta_trace[omega]);
            
            m_A_0_trace[omega] = Array<OneD, NekDouble>(nqTrace);
            m_fields[0]->ExtractTracePhys(m_A_0[omega],m_A_0_trace[omega]);
            if(SetToOneSpaceDimension)
            {
                m_trace_fwd_normal[omega] = Array<OneD, NekDouble>(nqTrace,0.0);
                
                MultiRegions::ExpListSharedPtr trace = m_fields[0]->GetTrace(); 
                int nelmt_trace = trace->GetExpSize();
                
                Array<OneD, Array<OneD, NekDouble> > normals(nelmt_trace);
            
                for(int i = 0 ; i < nelmt_trace; ++i)
                {
                    normals[i] = m_trace_fwd_normal[omega]+i;
                }
 
                // need to set to 1 for consistency since boundary
                // conditions may not have coordim=1
                trace->GetExp(0)->GetGeom()->SetCoordim(1); 
                
                trace->GetNormals(normals);
            }
        }
        SetUpDomainInterfaces();
        
   }

NekDouble Nektar::PulseWaveSystem::v_L2Error	(	unsigned int	field,
		const Array< OneD, NekDouble > &	exactsoln = `NullNekDouble1DArray`,
		bool	Normalised = `false`
	)

protectedvirtual

Compute the L2 error between fields and a given exact solution.

Reimplemented from Nektar::SolverUtils::EquationSystem.

Definition at line 1157 of file PulseWaveSystem.cpp.

References ASSERTL0, Nektar::SolverUtils::EquationSystem::EvaluateFunction(), Nektar::SolverUtils::EquationSystem::GetNpoints(), Nektar::SolverUtils::EquationSystem::m_comm, m_nDomains, Nektar::SolverUtils::EquationSystem::m_NumQuadPointsError, m_nVariables, Nektar::SolverUtils::EquationSystem::m_session, Nektar::SolverUtils::EquationSystem::m_time, m_vessels, and Nektar::LibUtilities::ReduceSum.

    {           
        NekDouble L2error = 0.0; 
        NekDouble L2error_dom;
        NekDouble Vol     = 0.0;
        if(m_NumQuadPointsError == 0)
        {
            for (int omega = 0; omega < m_nDomains; omega++)
            {
                int vesselid = field + omega*m_nVariables;
                
                if(m_vessels[vesselid]->GetPhysState() == false)
                {
                    m_vessels[vesselid]->BwdTrans(m_vessels[vesselid]->GetCoeffs(),
                                                  m_vessels[vesselid]->UpdatePhys());
                }
                
                if(exactsoln.num_elements())
                {
                    L2error_dom = m_vessels[vesselid]->L2(
                                        m_vessels[vesselid]->GetPhys(),
                                        exactsoln);
                }
                else if (m_session->DefinesFunction("ExactSolution"))
                {
                    Array<OneD, NekDouble> exactsoln(m_vessels[vesselid]->GetNpoints());
                    
                    LibUtilities::EquationSharedPtr vEqu
                        = m_session->GetFunction("ExactSolution",field,omega);
                    EvaluateFunction(m_session->GetVariable(field),exactsoln,"ExactSolution",
                                     m_time);
                    
                    L2error_dom = m_vessels[vesselid]->L2(
                                        m_vessels[vesselid]->GetPhys(),
                                        exactsoln);
                    
                }
                else
                {
                    L2error_dom = m_vessels[vesselid]->L2(
                                        m_vessels[vesselid]->GetPhys());
                }
                L2error += L2error_dom*L2error_dom;
                
                if(Normalised == true)
                {
                    Array<OneD, NekDouble> one(m_vessels[vesselid]->GetNpoints(), 1.0);
                    
                    Vol += m_vessels[vesselid]->PhysIntegral(one);
                }
                
            }
        }
        else
        {
            ASSERTL0(false,"Not set up");
        }
        
        
        if(Normalised == true)
        {
            m_comm->AllReduce(Vol, LibUtilities::ReduceSum);
        
            L2error = sqrt(L2error/Vol);
        }
        else
        {
            L2error = sqrt(L2error);
        }            
        
        return L2error;
    }

NekDouble Nektar::PulseWaveSystem::v_LinfError	(	unsigned int	field,
		const Array< OneD, NekDouble > &	exactsoln = `NullNekDouble1DArray`
	)

protectedvirtual

Compute the L_inf error between fields and a given exact solution.

Compute the error in the L_inf-norm

Parameters

field	The field to compare.
exactsoln	The exact solution to compare with.

Returns: Error in the L_inft-norm.

Reimplemented from Nektar::SolverUtils::EquationSystem.

Definition at line 1241 of file PulseWaveSystem.cpp.

References ASSERTL0, Nektar::SolverUtils::EquationSystem::EvaluateFunction(), Nektar::SolverUtils::EquationSystem::GetNpoints(), m_nDomains, Nektar::SolverUtils::EquationSystem::m_NumQuadPointsError, m_nVariables, Nektar::SolverUtils::EquationSystem::m_session, Nektar::SolverUtils::EquationSystem::m_time, and m_vessels.

    {
        NekDouble LinferrorDom, Linferror = -1.0;       
        
        for (int omega = 0; omega < m_nDomains; omega++)
        {
            int vesselid = field + omega*m_nVariables;
            if(m_NumQuadPointsError == 0)
            {
                if(m_vessels[vesselid]->GetPhysState() == false)
                {
                    m_vessels[vesselid]->BwdTrans(m_vessels[vesselid]->GetCoeffs(),
                                                  m_vessels[vesselid]->UpdatePhys());
                }
        
                if(exactsoln.num_elements())
                {
                    LinferrorDom = m_vessels[vesselid]->Linf(
                                        m_vessels[vesselid]->GetPhys(),
                                        exactsoln);
                }
                else if (m_session->DefinesFunction("ExactSolution"))
                {
                    Array<OneD, NekDouble> exactsoln(m_vessels[vesselid]->GetNpoints());
                    
                    EvaluateFunction(m_session->GetVariable(field),exactsoln,"ExactSolution",
                                     m_time);
                    
                    LinferrorDom = m_vessels[vesselid]->Linf(
                                        m_vessels[vesselid]->GetPhys(),
                                        exactsoln);
                }
                else
                {
                    LinferrorDom = 0.0;
                }
                Linferror = (Linferror > LinferrorDom)? Linferror:LinferrorDom;
                
            }
            else
            {
                ASSERTL0(false,"ErrorExtraPoints not allowed for this solver");
            }
        }
        return Linferror;
    }

void Nektar::PulseWaveSystem::v_Output ( void )

protectedvirtual

Writes the .fld file at the end of the simulation. Similar to the normal v_Output however the Multidomain output has to be prepared.

Write the field data to file. The file is named according to the session name with the extension .fld appended.

Reimplemented from Nektar::SolverUtils::EquationSystem.

Definition at line 1082 of file PulseWaveSystem.cpp.

References Nektar::SolverUtils::EquationSystem::m_sessionName, and WriteVessels().

    {
        /**
         * Write the field data to file. The file is named according to the session
         * name with the extension .fld appended.
         */
        std::string outname = m_sessionName + ".fld";
        WriteVessels(outname);  
    }

void Nektar::PulseWaveSystem::WriteVessels ( const std::string & outname )

protected

Write input fields to the given filename.

Writes the field data to a file with the given filename.

Parameters

outname Filename to write to.

Definition at line 1111 of file PulseWaveSystem.cpp.

References Nektar::SolverUtils::EquationSystem::m_fieldMetaDataMap, m_nDomains, m_nVariables, Nektar::SolverUtils::EquationSystem::m_session, Nektar::SolverUtils::EquationSystem::m_time, m_vessels, and Nektar::LibUtilities::Write().

Referenced by CheckPoint_Output(), and v_Output().

    {
        std::vector<LibUtilities::FieldDefinitionsSharedPtr> FieldDef;
        std::vector<std::string> variables = m_session->GetVariables();
        for(int n = 0; n < m_nDomains; ++n)
        {
            m_vessels[n*m_nVariables]->GetFieldDefinitions(FieldDef);
        }
        
        std::vector<std::vector<NekDouble> > FieldData(FieldDef.size());
        
        int nFieldDefPerDomain = FieldDef.size()/m_nDomains;
        int cnt;
        // Copy Data into FieldData and set variable
        for(int n = 0; n < m_nDomains; ++n)
        {
            for(int j = 0; j < m_nVariables; ++j)
            {
                for(int i = 0; i < nFieldDefPerDomain; ++i)
                {
                    cnt = n*nFieldDefPerDomain+i;
                    FieldDef[cnt]->m_fields.push_back(variables[j]);
                    m_vessels[n*m_nVariables]->AppendFieldData(FieldDef[cnt], FieldData[cnt], m_vessels[n*m_nVariables+j]->UpdateCoeffs());
                }
            }            
        }
        
        // Update time in field info if required
        if(m_fieldMetaDataMap.find("Time") != m_fieldMetaDataMap.end())
        {
            m_fieldMetaDataMap["Time"] =  boost::lexical_cast<std::string>(m_time); 
        }
        
        //LibUtilities::CombineFields(FieldDef, FieldData);
        
        LibUtilities::Write(outname, FieldDef, FieldData, m_fieldMetaDataMap);
    }    