van der Waals equation of state: p = RT/(1/rho - b) - a * rho^2 with a = 27/64 * (R*Tc)^2 / Pc b = 1/8 * (R*Tc) / Pc More...

#include <VanDerWaalsEoS.h>

Inheritance diagram for Nektar::VanDerWaalsEoS:

[legend]

Static Public Member Functions
static EquationOfStateSharedPtr	create (const LibUtilities::SessionReaderSharedPtr &pSession)
	Creates an instance of this class. More...

Static Public Attributes
static std::string	className
	Name of the class. More...

Protected Member Functions
virtual NekDouble	v_GetTemperature (const NekDouble &rho, const NekDouble &e)

virtual NekDouble	v_GetPressure (const NekDouble &rho, const NekDouble &e)

virtual NekDouble	v_GetEntropy (const NekDouble &rho, const NekDouble &e)

virtual NekDouble	v_GetDPDrho_e (const NekDouble &rho, const NekDouble &e)

virtual NekDouble	v_GetDPDe_rho (const NekDouble &rho, const NekDouble &e)

virtual NekDouble	v_GetEFromRhoP (const NekDouble &rho, const NekDouble &p)

virtual NekDouble	v_GetRhoFromPT (const NekDouble &rho, const NekDouble &p)

Protected Member Functions inherited from Nektar::EquationOfState
	EquationOfState (const LibUtilities::SessionReaderSharedPtr &pSession)
	Constructor. More...

virtual NekDouble	v_GetSoundSpeed (const NekDouble &rho, const NekDouble &e)

Protected Attributes
NekDouble	m_a

NekDouble	m_b

Protected Attributes inherited from Nektar::EquationOfState
NekDouble	m_gamma

NekDouble	m_gasConstant

Private Member Functions
	VanDerWaalsEoS (const LibUtilities::SessionReaderSharedPtr &pSession)

virtual	~VanDerWaalsEoS (void)

Friends
class	MemoryManager< VanDerWaalsEoS >

Additional Inherited Members
Public Member Functions inherited from Nektar::EquationOfState
virtual	~EquationOfState ()

NekDouble	GetTemperature (const NekDouble &rho, const NekDouble &e)
	Calculate the temperature. More...

NekDouble	GetPressure (const NekDouble &rho, const NekDouble &e)
	Calculate the pressure. More...

NekDouble	GetSoundSpeed (const NekDouble &rho, const NekDouble &e)
	Calculate the sound speed. More...

NekDouble	GetEntropy (const NekDouble &rho, const NekDouble &e)
	Calculate the entropy. More...

NekDouble	GetDPDrho_e (const NekDouble &rho, const NekDouble &e)
	Calculate the partial derivative of P(rho,e) with respect to rho. More...

NekDouble	GetDPDe_rho (const NekDouble &rho, const NekDouble &e)
	Calculate the partial derivative of P(rho,e) with respect to e. More...

NekDouble	GetEFromRhoP (const NekDouble &rho, const NekDouble &p)
	Obtain the internal energy from rho and P. More...

NekDouble	GetRhoFromPT (const NekDouble &p, const NekDouble &T)
	Obtain the density from P and T. More...

Detailed Description

van der Waals equation of state: p = RT/(1/rho - b) - a * rho^2 with a = 27/64 * (R*Tc)^2 / Pc b = 1/8 * (R*Tc) / Pc

Definition at line 49 of file VanDerWaalsEoS.h.

Constructor & Destructor Documentation

◆ VanDerWaalsEoS()

Nektar::VanDerWaalsEoS::VanDerWaalsEoS ( const LibUtilities::SessionReaderSharedPtr & pSession )

private

Definition at line 49 of file VanDerWaalsEoS.cpp.

References m_a, m_b, and Nektar::EquationOfState::m_gasConstant.

     : EquationOfState(pSession)
 {
     NekDouble Tcrit, Pcrit;
     pSession->LoadParameter("Tcrit", Tcrit);
     pSession->LoadParameter("Pcrit", Pcrit);
 
     m_a = 27.0 / 64.0 * m_gasConstant * m_gasConstant * Tcrit * Tcrit / Pcrit;
     m_b = 1.0 / 8.0 * m_gasConstant * Tcrit / Pcrit;
 }

◆ ~VanDerWaalsEoS()

virtual Nektar::VanDerWaalsEoS::~VanDerWaalsEoS ( void )

inlineprivatevirtual

Definition at line 88 of file VanDerWaalsEoS.h.

88 {};

Member Function Documentation

◆ create()

static EquationOfStateSharedPtr Nektar::VanDerWaalsEoS::create ( const LibUtilities::SessionReaderSharedPtr & pSession )

inlinestatic

Creates an instance of this class.

Definition at line 55 of file VanDerWaalsEoS.h.

References Nektar::MemoryManager< DataType >::AllocateSharedPtr(), and CellMLToNektar.cellml_metadata::p.

     {
         EquationOfStateSharedPtr p =
             MemoryManager<VanDerWaalsEoS>::AllocateSharedPtr(pSession);
         return p;
     }

◆ v_GetDPDe_rho()

NekDouble Nektar::VanDerWaalsEoS::v_GetDPDe_rho	(	const NekDouble &	rho,
		const NekDouble &	e
	)

protectedvirtual

Implements Nektar::EquationOfState.

Definition at line 95 of file VanDerWaalsEoS.cpp.

References m_b, and Nektar::EquationOfState::m_gamma.

 {
     boost::ignore_unused(e);
     return (m_gamma - 1) / (1.0 / rho - m_b);
 }

◆ v_GetDPDrho_e()

NekDouble Nektar::VanDerWaalsEoS::v_GetDPDrho_e	(	const NekDouble &	rho,
		const NekDouble &	e
	)

protectedvirtual

Implements Nektar::EquationOfState.

Definition at line 83 of file VanDerWaalsEoS.cpp.

References m_a, m_b, and Nektar::EquationOfState::m_gamma.

 {
     NekDouble result;
 
     result = (m_gamma - 1) * (e + 2 * m_a * rho - m_a * m_b * rho * rho);
     result = result / ((1 - m_b * rho) * (1 - m_b * rho));
     result = result - 2 * m_a * rho;
 
     return result;
 }

◆ v_GetEFromRhoP()

NekDouble Nektar::VanDerWaalsEoS::v_GetEFromRhoP	(	const NekDouble &	rho,
		const NekDouble &	p
	)

protectedvirtual

Implements Nektar::EquationOfState.

Definition at line 102 of file VanDerWaalsEoS.cpp.

References m_a, m_b, and Nektar::EquationOfState::m_gamma.

 {
     return (p + m_a * rho * rho) * (1.0 / rho - m_b) / (m_gamma - 1) -
            m_a * rho;
 }

◆ v_GetEntropy()

NekDouble Nektar::VanDerWaalsEoS::v_GetEntropy	(	const NekDouble &	rho,
		const NekDouble &	e
	)

protectedvirtual

Implements Nektar::EquationOfState.

Definition at line 74 of file VanDerWaalsEoS.cpp.

References Nektar::EquationOfState::GetTemperature(), m_b, Nektar::EquationOfState::m_gamma, and Nektar::EquationOfState::m_gasConstant.

 {
     NekDouble T = GetTemperature(rho, e);
     NekDouble sIg =
         m_gasConstant / (m_gamma - 1) * log(T) - m_gasConstant * log(rho);
 
     return sIg + m_gasConstant * log(1 - m_b * rho);
 }

◆ v_GetPressure()

NekDouble Nektar::VanDerWaalsEoS::v_GetPressure	(	const NekDouble &	rho,
		const NekDouble &	e
	)

protectedvirtual

Implements Nektar::EquationOfState.

Definition at line 67 of file VanDerWaalsEoS.cpp.

References m_a, m_b, and Nektar::EquationOfState::m_gamma.

 {
     return (e + m_a * rho) * (m_gamma - 1) / (1.0 / rho - m_b) -
            m_a * rho * rho;
 }

◆ v_GetRhoFromPT()

NekDouble Nektar::VanDerWaalsEoS::v_GetRhoFromPT	(	const NekDouble &	rho,
		const NekDouble &	p
	)

protectedvirtual

Implements Nektar::EquationOfState.

Definition at line 109 of file VanDerWaalsEoS.cpp.

References m_a, m_b, and Nektar::EquationOfState::m_gasConstant.

 {
     // First solve for the compressibility factor Z using the cubic equation
     //    Z^3 + k1 * Z^2 + k2 * Z + k3 = 0
     //    for van der Waals:
     //        k1 = -(B+1), k2 = A,  k3 = -AB
     //    where A = aP/(RT)^2, B = bP/(RT)
     NekDouble A = m_a * p / (m_gasConstant * m_gasConstant * T * T);
     NekDouble B = m_b * p / (m_gasConstant * T);
 
     NekDouble k1 = -(B + 1);
     NekDouble k2 = A;
     NekDouble k3 = -A * B;
 
     // Use ideal gas (Z=1) as starting guess for iteration
     NekDouble Z = 1.0;
     // Newton-Raphson iteration to find Z
     NekDouble tol      = 1e-6;
     NekDouble maxIter  = 100;
     NekDouble residual = 1;
     NekDouble f, df;
     unsigned int cnt = 0;
     while (abs(residual) > tol && cnt < maxIter)
     {
         f        = Z * Z * Z + k1 * Z * Z + k2 * Z + k3;
         df       = 3 * Z * Z + 2 * k1 * Z + k2;
         residual = f / df;
         Z -= residual;
         ++cnt;
     }
     if (cnt == maxIter)
     {
         cout << "Newton-Raphson in VanDerWaalsEoS::v_GetRhoFromPT did not "
                 "converge in "
              << maxIter << " iterations (residual = " << residual << ")"
              << endl;
     }
 
     // Now calculate rho = p/(ZRT)
     return p / (Z * m_gasConstant * T);
 }

◆ v_GetTemperature()

NekDouble Nektar::VanDerWaalsEoS::v_GetTemperature	(	const NekDouble &	rho,
		const NekDouble &	e
	)

protectedvirtual

Implements Nektar::EquationOfState.

Definition at line 61 of file VanDerWaalsEoS.cpp.

References m_a, Nektar::EquationOfState::m_gamma, and Nektar::EquationOfState::m_gasConstant.

 {
     return (e + m_a * rho) * (m_gamma - 1) / m_gasConstant;
 }

Friends And Related Function Documentation

◆ MemoryManager< VanDerWaalsEoS >

friend class MemoryManager< VanDerWaalsEoS >

friend

Definition at line 52 of file VanDerWaalsEoS.h.

Member Data Documentation

◆ className

std::string Nektar::VanDerWaalsEoS::className

static

Initial value:

=
    GetEquationOfStateFactory().RegisterCreatorFunction(
        "VanDerWaals", VanDerWaalsEoS::create,
        "Van der Waals equation of state.")

Name of the class.

Definition at line 64 of file VanDerWaalsEoS.h.

◆ m_a

NekDouble Nektar::VanDerWaalsEoS::m_a

protected

Definition at line 67 of file VanDerWaalsEoS.h.

Referenced by v_GetDPDrho_e(), v_GetEFromRhoP(), v_GetPressure(), v_GetRhoFromPT(), v_GetTemperature(), and VanDerWaalsEoS().

◆ m_b

NekDouble Nektar::VanDerWaalsEoS::m_b

protected

Definition at line 68 of file VanDerWaalsEoS.h.

Referenced by v_GetDPDe_rho(), v_GetDPDrho_e(), v_GetEFromRhoP(), v_GetEntropy(), v_GetPressure(), v_GetRhoFromPT(), and VanDerWaalsEoS().

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Private Member Functions

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ VanDerWaalsEoS()

◆ ~VanDerWaalsEoS()

Member Function Documentation

◆ create()

◆ v_GetDPDe_rho()

◆ v_GetDPDrho_e()

◆ v_GetEFromRhoP()

◆ v_GetEntropy()

◆ v_GetPressure()

◆ v_GetRhoFromPT()

◆ v_GetTemperature()

Friends And Related Function Documentation

◆ MemoryManager< VanDerWaalsEoS >

Member Data Documentation

◆ className

◆ m_a

◆ m_b