6.3 Session file configuration

Parameters

Under this section it is possible to set the parameters of the simulation.

1<PARAMETERS>
2  <P> TimeStep       = 1e-05  /P>
3  <P> NumSteps       = 1000   /P>
4  <P> FinTime        = 0.01   /P>
5  <P> IO_CheckSteps  = 100    /P>
6  <P> IO_InfoSteps   = 10     /P>
7  <P> IO_CFLSteps    = 10     /P>
8</PARAMETERS>
• TimeStep is the time-step we want to use;
• FinTime is the final physical time at which we want our simulation to stop;
• NumSteps is the equivalent of FinTime but instead of specifying the physical final time we specify the number of time-steps;
• IO_CheckSteps sets the number of steps between successive checkpoint files;
• IO_InfoSteps sets the number of steps between successive info stats are printed to screen;
• IO_CFLSteps sets the number of steps between successive Courant number stats are printed to screen;

6.3.1 Time Integration Scheme

1<TIMEINTEGRATIONSCHEME>
2  <METHOD> RungeKutta </METHOD>
3  <VARIANT> SSP </VARIANT>
4  <ORDER> 3 </ORDER>
5</TIMEINTEGRATIONSCHEME>
• Method is the time-integration method. Note that only an explicit discretisation is supported.
• Order is the order of the time-integration method.
• Variant is the variant of the time-integration method (variables for Runga Kutta: Blank, SSP).

6.3.2 Solver Info

1<SOLVERINFO>
2  <I PROPERTY="EQType"                VALUE="APE"                  />
3  <I PROPERTY="Projection"            VALUE="DisContinuous"        />
4  <I PROPERTY="UpwindType"            VALUE="LaxFriedrichs"        />
5</SOLVERINFO>
• EQType is the tag which specify the equations we want solve:
• APE Acoustic Perturbation Equations (variables: p,u,v,w);
• LEE Linearized Euler Equations (variables: p,rho,rhou,rhov,rhow).
• Projection is the type of projection we want to use. Currently, only DisContinuous is supported.
• AdvectionType is the advection operator. Currently, only WeakDG (classical DG in weak form) is supported.
• UpwindType is the numerical interface flux (i.e. Riemann solver) we want to use for the advection operator (see [24] for the implemented formulations):
• Upwind;
• LaxFriedrichs;

6.3.3 Variables

For the APE operator, the acoustic pressure and velocity perturbations are solved, e.g.:

1<VARIABLES>
2  <V ID="0"> p </V>
3  <V ID="1"> u </V>
4  <V ID="2"> v </V>
5  <V ID="3"> w </V>
6</VARIABLES>

The LEE use a conservative formulation and introduce the additional density perturbation:

1<VARIABLES>
2  <V ID="0"> p    </V>
3  <V ID="1"> rho  </V>
4  <V ID="2"> rhou </V>
5  <V ID="3"> rhov </V>
6  <V ID="4"> rhow </V>
7</VARIABLES>

6.3.4 Functions

• BaseFlow Baseflow (ρ,c2,u) defined by the variables rho0, c0sq, u0, v0, w0 for APE and (ρ,c2,u, γ) defined by rho0, c0sq, u0, v0, w0, gamma for LEE.
• InitialConditions

6.3.5 Boundary Conditions

In addition to plain Dirichlet and Neumann boundary conditions, the AcousticSolver features a slip-wall boundary condition, a non-reflecting boundary and a white noise boundary condition.

• Rigid (Slip-) Wall Boundary Condition, e.g. for APE:
1<BOUNDARYCONDITIONS>
2<REGION REF="0">
3    <D VAR="p" USERDEFINEDTYPE="Wall" VALUE="0" />
4    <D VAR="u" USERDEFINEDTYPE="Wall" VALUE="0" />
5    <D VAR="v" USERDEFINEDTYPE="Wall" VALUE="0" />
6    <D VAR="w" USERDEFINEDTYPE="Wall" VALUE="0" />
7</REGION>
8</BOUNDARYCONDITIONS>

This BC imposes zero wall-normal perturbation velocity in a way that is more robust than using a Dirichlet boundary condition directly.

• Non-Reflecting Boundary Condition, e.g. for APE:
1<BOUNDARYCONDITIONS>
2<REGION REF="0">
3    <D VAR="p" USERDEFINEDTYPE="RiemannInvariantBC"/>
4    <D VAR="u" USERDEFINEDTYPE="RiemannInvariantBC"/>
5    <D VAR="v" USERDEFINEDTYPE="RiemannInvariantBC"/>
6    <D VAR="w" USERDEFINEDTYPE="RiemannInvariantBC"/>
7</REGION>
8</BOUNDARYCONDITIONS>

The Riemann-Invariant BC approximates a non-reflecting (r.g. Farfield) boundary condition by setting incoming invariants to zero.

• White Noise Boundary Condition, e.g. for APE:
1<BOUNDARYCONDITIONS>
2<REGION REF="0">
3    <D VAR="p" USERDEFINEDTYPE="Wall" VALUE="10" />
4    <D VAR="u" USERDEFINEDTYPE="Wall" VALUE="10" />
5    <D VAR="v" USERDEFINEDTYPE="Wall" VALUE="10" />
6    <D VAR="w" USERDEFINEDTYPE="Wall" VALUE="10" />
7</REGION>
8</BOUNDARYCONDITIONS>

The white noise BC imposes a stochastic, uniform pressure at the boundary. The implementation uses a Mersenne-Twister pseudo random number generator to generate white Gaussian noise. The standard deviation σ of the pressure is specified by the VALUE attribute.