Numerical Flux Functions

Numerical Flux Functions

This page documents the numerical flux functions available in the code

bc_solvers.jl should be renamed to this

EulerEquationMod.RoeSolver — Method.

EulerEquationMod.RoeSolver

This calculates the Roe flux for boundary conditions at a node. The inputs must be in conservative variables.

Inputs

  • params : ParamType

  • q : conservative variables of the fluid

  • qg : conservative variables of the boundary

  • aux_vars : vector of all auxiliary variables at this node

  • nrm : scaled face normal vector (x-y space, outward normal of the face q lives on)

Outputs

  • flux : vector to populate with solution

Aliasing restrictions: none of the inputs can alias params.res_vals1, params.res_vals2, params.q_vals, params.flux_vals1, or params.sat

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EulerEquationMod.RoeSolver — Method.

The main Roe solver. Populates flux with the computed flux.

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EulerEquationMod.RoeSolver_revm — Method.

###EulerEquationMod.RoeSolver_revm

Reverse mode of EulerEquationMod.RoeSolver. This function computes the reverse mode of the Roe flux w.r.t the mesh metrics

Inputs

  • params : Parameter object

  • q : Conservative variable of the fluid

  • qg : Conservative variable of the boundary or the adjacent element

  • aux_vars : Auxiliary variables

  • nrm : Element face normal vector in the physical space

  • flux_bar : Flux value which needs to get differentiated

Output

  • nrm_bar : derivaitve of the flux_bar w.r.t the mesh metrics

Aliasing Restrictions: Same as the forward function

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EulerEquationMod.calcEulerFlux_Ducros — Method.

Calculates the numerical flux function associated with the Ducros flux splitting. Methods are available for 2D and 3D.

Inputs:

  • params:

  • qL: the left state

  • qR: the right state

  • aux_vars: the aux vars for the left state

  • dir: the direction vector

Inputs/Outputs:

  • F: vector to be populated with the flux

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EulerEquationMod.calcEulerFlux_IR — Method.

This function calculates the Ismail-Roe numerical flux at a node in a specified direction

Inputs:

  • params: ParamType

  • qL: left state vector

  • qR: right state vector

  • aux_vars: auxiliary variable vector for qL

  • dir: a direction vector of length Tdim

Inputs/Outputs:

  • F: a numDofPerNode x Tdim matrix where each column will be populated with the flux in the direction specified by the corresponding column of nrm

Aliasing Restrictions: none

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EulerEquationMod.calcEulerFlux_IR — Method.

This function computes the Ismail-Roe flux in Tdim directions at once for a given state. This is more efficient Than calling the single direction method Tdim times. Methods are available for 2 and 3 dimensions.

Inputs:

  • params: ParamType

  • qL: left state vector

  • qR: right state vector

  • aux_vars: auxiliary variable vector for qL

  • dir: a Tdim x Tdim matrix with each column containing a normal vector

Inputs/Outputs:

  • F: a numDofPerNode x Tdim matrix where each column will be populated with the flux in the direction specified by the corresponding column of nrm

Aliasing restrictions: none

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EulerEquationMod.calcEulerFlux_IRSLF — Method.

This is the second method that takes in a normal vector directly. See the first method for a description of what this function does.

Inputs qL, qR: vectors conservative variables at left and right states aux_vars: aux_vars for qL nrm: a normal vector in xy space

Inputs/Outputs F: vector to be updated with the result

Alising restrictions: See getEntropyLFStab

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EulerEquationMod.calcEulerFlux_IRSLW — Method.

This function is similar to calcEulerFlux_IRSLF, but uses Lax-Wendroff dissipation rather than Lax-Friedrich.

Aliasing restrictions: see getEntropyLWStab

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EulerEquationMod.calcEulerFlux_standard — Method.

This function computes the split form flux corresponding to the standard flux in Tdim directions at once for a given state. This is more efficient Than calling the single direction method Tdim times. Methods are available for 2 and 3 dimensions.

Inputs: params: ParamType qL: left state vector qR: right state vector aux_vars: auxiliary variable vector for qL dir: a Tdim x Tdim matrix with each column containing a normal vector

Inputs/Outputs: F: a numDofPerNode x Tdim matrix where each column will be populated with the flux in the direction specified by the corresponding column of nrm

Aliasing restrictions: none

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EulerEquationMod.calcLFFlux — Method.

Calculates the Lax-Friedrich flux function on the conservative variables

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EulerEquationMod.calcSAT — Method.

###EulerEquationMod.calcSAT

Computes the simultaneous approximation term for use in computing the numerical flux, namely:

0.5*(|A_hat| - A)(qL - qR)

Arguments

  • params : Parameter object of type ParamType

  • `roe_vars: [u, v, H] at roe average state

  • dq : difference between left and right states

  • nrm : Normal to face in the physical space

  • sat : Simultaneous approximation Term

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EulerEquationMod.calcSAT_revm — Method.

###EulerEquationMod.calcSAT_revm

Reverse mode of calcSAT

Inputs

  • params : Parameter object of type ParamType

  • nrm : Normal to face in the physical space

  • dq : Boundary condition penalty variable

  • vel : Velocities along X & Y directions in the physical space

  • H : Total enthalpy

  • sat_bar : Inpute seed for sat flux whose derivative needs to be computed

Output

  • nrm_bar : derivative of sat_bar w.r.t physical normal vector

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