
Quick search Spatial Schemes¶ The modules defining spatial schemes are located in the folder `_Solver/SpatialSchemes`. Each module defining a spatial scheme should comport a class `Scheme` within which at least the methods `ComputeFlux`, `Iteration`, `ReconstructSolutionAtVertices` are implemented. Each module should also comport a class `AssociatedMeshType` comporting the fields `MeshType`, `MeshOrder` and `ControlVolumes` that will be used to select the relevant mesh and compute properly the mass lumping. Already implemented schemes Continuous galerkin + Lax-Friedrichs Continuous galerkin + Lax-Friedrichs ¶ class `3_LESARD.SourceCode._Solver.SpatialSchemes.CG_LFX.AssociatedMeshType`(SchemeParams=[1])¶ Class that only gives out the mesh type that should be loaded when tackling the problem with this scheme, given the wished variational order. Access the associated mesh properties through the inner variables MeshType (string) – the mesh type according to fenics’s classification MeshOrder (integer) – the mesh order Note This is only a product-type class: no method is available Parameters SchemeParams (string list, optional) – the parameters of the spatial scheme wished by the user class `3_LESARD.SourceCode._Solver.SpatialSchemes.CG_LFX.Scheme`(Problem, Mesh, QuadratureRules, SchemeParams)¶ Class furnishing all the schemes tools and registers the scheme’s wished parameters. The main iteration is accessible with the method “Iteration”. Repeats the instance’s initialisation arguments as fields with identical names within the structure. Has for additional field upon instance creation the fields: Order* (integer) – The order of the used basis functions InnerQBFValues (float numpy array) – Value of the basis function at the quadrature points of each element (NbInnerElementsx NbQuadraturePoints x NbBasisFunc) InnerQWeigths (float numpy array) – Weights of the quadrature points of each element (NbInnerElements x NbQuadraturePoints) InnerQGFValues (float numpy array) – Value of the gradient of the basis function at the quadrature points of each element (NbInnerElements x NbQuadraturePoints x NbBasisFunc x dim) InnerQPoints (float numpy array) – Quadrature points of each element (NbInnerElements x NbQuadraturePoints) FaceWiseQWeigths (float numpy array) – Weights of the quadrature points of each element’s face (NbInnerElements x NbFace x NbQuadraturePoints) FaceWiseQPoints (float numpy array) – Quadrature points of each element’s face (NbInnerElements x NbFace x NbQuadraturePoints) FaceWiseQBFValues (float numpy array) – Value of the basis function at the quadrature points of each element’s face (NbInnerElements x NbFace x NbQuadraturePoints x NbBasisFunc) Parameters Problem (Problem) – the considered problem Mesh (MeshStructure) – the considered mesh instance QuadratureRules (Quadratures) – the quadratures to use within the scheme. SchemeParams (string list) – the scheme’s parameters as wished by the user Methods `ComputeFlux`(FlagPoints, U, LSValues)¶ Emulates a flux computation as done in the iteration routine in order to be used in the DeC subtimestep evaluation. Parameters FlagPoints (function callback) – mapper to the routine of the FluidSpotter FlagPoints method to flag the Fluid on given points according the given LSValues at Dofs U (numpy float array) – buffer containing the current state values at each dof (NbVars x NbDofs) LSValues (numpy float array) – buffer containing the current FluidSpotters values at each dof(NbFluids x NbDofs) Returns fluxes in the format required by the Iteration routine Return type fluxes (numpy float (multiD)array) `Iteration`(FlagPoints, Solution, fluxes, i, du=0, dt=1)¶ Main iteration of the scheme, implementing the most stupid scheme you can think of. Parameters FlagPoints (function callback) – the handle of a function flagging the points to the relevant fluid Solution (solution structure) – structure containing the current solution’s values to iterate fluxes (numpy (multiD)array) – pre-computed fluxes at the points of interest. For this scheme, access with fluxes[element, face, coordinate(fx or fy), variable, pointindex] i (integer) – the index of the considered element within which the partial residuals will be computed du (float numpy array) – (optional) when using DeC, the difference in the time iteration dt (float) – (optional) when using DeC, the full time step Returns the computed residuals (NbVars x NbDofs) Return type Resu (float numpy array) `ReconstructSolutionAtVertices`(Solution)¶ Routine that maps the values from the Dofs to the Physical vertices of the mesh of the solution. Parameters Solution (Solution) – the currently being computed solution Returns fills direclty the RSol and RFluidFlag values in the data structure Return type None Note This is only for later plotting purposes. `PreEvaluateQuadratureQuantities`()¶ Precomputing and storing the values of the basis functions at the quadrature points of each element Parameters None – Considers the given parameters of the class directly Returns Creates the fields InnerQBFValues, InnerQWeigths, InnerQGFValues, InnerQPoints, FaceWiseQWeigths, FaceWiseQPoints and FaceWiseQBFValues in the scheme structure, containing the values of each basis function at each quadrature point for each element and face. Return type None class `3_LESARD.SourceCode._Solver.SpatialSchemes.CG.AssociatedMeshType`(SchemeParams=[1])¶ Class that only gives out the mesh type that should be loaded when tackling the problem with this scheme, given the wished variational order. Access the associated mesh properties through the inner variables MeshType (string) – the mesh type according to fenics’s classification MeshOrder (integer) – the mesh order Note This is only a product-type class: no method is available Parameters SchemeParams (string list, optional) – the parameters of the spatial scheme wished by the user class `3_LESARD.SourceCode._Solver.SpatialSchemes.CG.Scheme`(Problem, Mesh, QuadratureRules, SchemeParams)¶ Class furnishing all the schemes tools and registers the scheme’s wished parameters. The main iteration is accessible with the method “Iteration”. Repeats the instance’s initialisation arguments as fields with identical names within the structure. Has for additional field upon instance creation the fields: Order* (integer) – The order of the used basis functions InnerQBFValues (float numpy array) – Value of the basis function at the quadrature points of each element (NbInnerElementsx NbQuadraturePoints x NbBasisFunc) InnerQWeigths (float numpy array) – Weights of the quadrature points of each element (NbInnerElements x NbQuadraturePoints) InnerQGFValues (float numpy array) – Value of the gradient of the basis function at the quadrature points of each element (NbInnerElements x NbQuadraturePoints x NbBasisFunc x dim) InnerQPoints (float numpy array) – Quadrature points of each element (NbInnerElements x NbQuadraturePoints) FaceWiseQWeigths (float numpy array) – Weights of the quadrature points of each element’s face (NbInnerElements x NbFace x NbQuadraturePoints) FaceWiseQPoints (float numpy array) – Quadrature points of each element’s face (NbInnerElements x NbFace x NbQuadraturePoints) FaceWiseQBFValues (float numpy array) – Value of the basis function at the quadrature points of each element’s face (NbInnerElements x NbFace x NbQuadraturePoints x NbBasisFunc) Parameters Problem (Problem) – the considered problem Mesh (MeshStructure) – the considered mesh instance QuadratureRules (Quadratures) – the quadratures to use within the scheme. SchemeParams (string list) – the scheme’s parameters as wished by the user Methods `ComputeFlux`(FlagPoints, U, LSValues)¶ Emulates a flux computation as done in the iteration routine in order to be used in the DeC subtimestep evaluation. Parameters FlagPoints (function callback) – mapper to the routine of the FluidSpotter FlagPoints method to flag the Fluid on given points according the given LSValues at Dofs U (numpy float array) – buffer containing the current state values at each dof (NbVars x NbDofs) LSValues (numpy float array) – buffer containing the current FluidSpotters values at each dof(NbFluids x NbDofs) Returns fluxes in the format required by the Iteration routine Return type fluxes (numpy float (multiD)array) `Iteration`(FlagPoints, Solution, fluxes, i, du=0, dt=1)¶ Main iteration of the scheme, implementing the most stupid scheme you can think of. Parameters FlagPoints (function callback) – the handle of a function flagging the points to the relevant fluid (not used here) Solution (solution structure) – structure containing the current solution’s values to iterate fluxes (numpy (multiD)array) – pre-computed fluxes at the points of interest. For this scheme, access with fluxes[element, face, coordinate(fx or fy), variable, pointindex] i (integer) – the index of the considered element within which the partial residuals will be computed du (float numpy array) – (optional) when using DeC, the difference in the time iteration dt (float) – (optional) when using DeC, the full time step Returns the computed residuals (NbVars x NbDofs) Return type Resu (float numpy array) `ReconstructSolutionAtVertices`(Solution)¶ Routine that maps the values from the Dofs to the Physical vertices of the mesh of the solution. Parameters Solution (Solution) – the currently being computed solution Returns fills direclty the RSol and RFluidFlag values in the data structure Return type None Note This is only for later plotting purposes. `PreEvaluateQuadratureQuantities`()¶ Precomputing and storing the values of the basis functions at the quadrature points of each element Parameters None – Considers the given parameters of the class directly Returns Creates the fields InnerBFValues and FaceWiseBFValues in the scheme structure, containing the values of each basis function at each quadrature point for each element and face. Return type None class `3_LESARD.SourceCode._Solver.SpatialSchemes.CG_Primary.AssociatedMeshType`(SchemeParams=[1])¶ Class that only gives out the mesh type that should be loaded when tackling the problem with this scheme, given the wished variational order. Access the associated mesh properties through the inner variables MeshType (string) – the mesh type according to fenics’s classification MeshOrder (integer) – the mesh order Note This is only a product-type class: no method is available Parameters SchemeParams (string list, optional) – the parameters of the spatial scheme wished by the user class `3_LESARD.SourceCode._Solver.SpatialSchemes.CG_Primary.Scheme`(Problem, Mesh, QuadratureRules, SchemeParams)¶ Class furnishing all the schemes tools and registers the scheme’s wished parameters. The main iteration is accessible with the method “Iteration”. Repeats the instance’s initialisation arguments as fields with identical names within the structure.Has for additional field upon instance creation the fields: Order* (integer) – The order of the used basis functions InnerQBFValues (float numpy array) – Value of the basis function at the quadrature points of each element (NbInnerElementsx NbQuadraturePoints x NbBasisFunc) InnerQWeigths (float numpy array) – Weights of the quadrature points of each element (NbInnerElements x NbQuadraturePoints) InnerQGFValues (float numpy array) – Value of the gradient of the basis function at the quadrature points of each element (NbInnerElements x NbQuadraturePoints x NbBasisFunc x dim) InnerQPoints (float numpy array) – Quadrature points of each element (NbInnerElements x NbQuadraturePoints) FaceWiseQWeigths (float numpy array) – Weights of the quadrature points of each element’s face (NbInnerElements x NbFace x NbQuadraturePoints) FaceWiseQPoints (float numpy array) – Quadrature points of each element’s face (NbInnerElements x NbFace x NbQuadraturePoints) FaceWiseQBFValues (float numpy array) – Value of the basis function at the quadrature points of each element’s face (NbInnerElements x NbFace x NbQuadraturePoints x NbBasisFunc) Note This scheme is the CG one where the variables interpolated are rho, rhoU, rhoV, p instead of the conservative ones, in order to preserve the pressure contacts if any Parameters Problem (Problem) – the considered problem Mesh (MeshStructure) – the considered mesh instance QuadratureRules (Quadratures) – the quadratures to use within the scheme. SchemeParams (string list) – the scheme’s parameters as wished by the user Methods `ComputeFlux`(FlagPoints, U, LSValues)¶ Emulates a flux computation as done in the iteration routine in order to be used in the DeC subtimestep evaluation. Parameters FlagPoints (function callback) – mapper to the routine of the FluidSpotter FlagPoints method to flag the Fluid on given points according the given LSValues at Dofs U (numpy float array) – buffer containing the current state values at each dof (NbVars x NbDofs) LSValues (numpy float array) – buffer containing the current FluidSpotters values at each dof(NbFluids x NbDofs) Returns fluxes in the format required by the Iteration routine Return type fluxes (numpy float (multiD)array) `Iteration`(FlagPoints, Solution, fluxes, i, du=0, dt=1)¶ Main iteration of the scheme, implementing the most stupid scheme you can think of. Parameters FlagPoints (function callback) – the handle of a function flagging the points to the relevant fluid (not used here) Solution (solution structure) – structure containing the current solution’s values to iterate fluxes (numpy (multiD)array) – pre-computed fluxes at the points of interest. For this scheme, access with fluxes[element, face, coordinate(fx or fy), variable, pointindex] i (integer) – the index of the considered element within which the partial residuals will be computed du (float numpy array) – (optional) when using DeC, the difference in the time iteration dt (float) – (optional) when using DeC, the full time step Returns the computed residuals (NbVars x NbDofs) Return type Resu (float numpy array) `ReconstructSolutionAtVertices`(Solution)¶ Routine that maps the values from the Dofs to the Physical vertices of the mesh of the solution. Parameters Solution (Solution) – the currently being computed solution Returns fills direclty the RSol and RFluidFlag values in the data structure Return type None Note This is only for later plotting purposes. `PreEvaluateQuadratureQuantities`()¶ Precomputing and storing the values of the basis functions at the quadrature points of each element Parameters None – Considers the given parameters of the class directly Returns Creates the fields InnerBFValues and FaceWiseBFValues in the scheme structure, containing the values of each basis function at each quadrature point for each element and face. Return type None

Spatial Schemes¶

The modules defining spatial schemes are located in the folder _Solver/SpatialSchemes.

Each module defining a spatial scheme should comport a class Scheme within which at least the methods ComputeFlux, Iteration, ReconstructSolutionAtVertices are implemented.

Each module should also comport a class AssociatedMeshType comporting the fields MeshType, MeshOrder and ControlVolumes that will be used to select the relevant mesh and compute properly the mass lumping.

Already implemented schemes

Continuous galerkin + Lax-Friedrichs

Continuous galerkin + Lax-Friedrichs ¶

class 3_LESARD.SourceCode._Solver.SpatialSchemes.CG_LFX.AssociatedMeshType(SchemeParams=[1])¶

Class that only gives out the mesh type that should be loaded when tackling the problem with this scheme, given the wished variational order. Access the associated mesh properties through the inner variables

MeshType (string) – the mesh type according to fenics’s classification

MeshOrder (integer) – the mesh order

Note

This is only a product-type class: no method is available

Parameters: SchemeParams (string list, optional) – the parameters of the spatial scheme wished by the user

class 3_LESARD.SourceCode._Solver.SpatialSchemes.CG_LFX.Scheme(Problem, Mesh, QuadratureRules, *SchemeParams)¶

Class furnishing all the schemes tools and registers the scheme’s wished parameters. The main iteration is accessible with the method “Iteration”.

Repeats the instance’s initialisation arguments as fields with identical names within the structure. Has for additional field upon instance creation the fields:

Order (integer) – The order of the used basis functions

InnerQBFValues (float numpy array) – Value of the basis function at the quadrature points of each element (NbInnerElementsx NbQuadraturePoints x NbBasisFunc)

InnerQWeigths (float numpy array) – Weights of the quadrature points of each element (NbInnerElements x NbQuadraturePoints)

InnerQGFValues (float numpy array) – Value of the gradient of the basis function at the quadrature points of each element (NbInnerElements x NbQuadraturePoints x NbBasisFunc x dim)

InnerQPoints (float numpy array) – Quadrature points of each element (NbInnerElements x NbQuadraturePoints)

FaceWiseQWeigths (float numpy array) – Weights of the quadrature points of each element’s face (NbInnerElements x NbFace x NbQuadraturePoints)

FaceWiseQPoints (float numpy array) – Quadrature points of each element’s face (NbInnerElements x NbFace x NbQuadraturePoints)

FaceWiseQBFValues (float numpy array) – Value of the basis function at the quadrature points of each element’s face (NbInnerElements x NbFace x NbQuadraturePoints x NbBasisFunc)

Parameters

Problem (Problem) – the considered problem
Mesh (MeshStructure) – the considered mesh instance
QuadratureRules (Quadratures) – the quadratures to use within the scheme.
SchemeParams (string list) – the scheme’s parameters as wished by the user

Methods

ComputeFlux(FlagPoints, U, LSValues)¶

Emulates a flux computation as done in the iteration routine in order to be used in the DeC subtimestep evaluation.

Parameters

FlagPoints (function callback) – mapper to the routine of the FluidSpotter FlagPoints method to flag the Fluid on given points according the given LSValues at Dofs
U (numpy float array) – buffer containing the current state values at each dof (NbVars x NbDofs)
LSValues (numpy float array) – buffer containing the current FluidSpotters values at each dof(NbFluids x NbDofs)

Returns

fluxes in the format required by the Iteration routine

Return type

fluxes (numpy float (multiD)array)

Iteration(FlagPoints, Solution, fluxes, i, du=0, dt=1)¶

Main iteration of the scheme, implementing the most stupid scheme you can think of.

Parameters

FlagPoints (function callback) – the handle of a function flagging the points to the relevant fluid
Solution (solution structure) – structure containing the current solution’s values to iterate
fluxes (numpy (multiD)array) – pre-computed fluxes at the points of interest. For this scheme, access with fluxes[element, face, coordinate(fx or fy), variable, pointindex]
i (integer) – the index of the considered element within which the partial residuals will be computed
du (float numpy array) – (optional) when using DeC, the difference in the time iteration
dt (float) – (optional) when using DeC, the full time step

Returns

the computed residuals (NbVars x NbDofs)

Return type

Resu (float numpy array)

ReconstructSolutionAtVertices(Solution)¶

Routine that maps the values from the Dofs to the Physical vertices of the mesh of the solution.

Parameters: Solution (Solution) – the currently being computed solution
Returns: fills direclty the RSol and RFluidFlag values in the data structure
Return type: None

Note

This is only for later plotting purposes.

PreEvaluateQuadratureQuantities()¶

Precomputing and storing the values of the basis functions at the quadrature points of each element

Parameters

None – Considers the given parameters of the class directly

Returns

Creates the fields InnerQBFValues, InnerQWeigths, InnerQGFValues, InnerQPoints, FaceWiseQWeigths,: FaceWiseQPoints and FaceWiseQBFValues in the scheme structure, containing the values of each basis function at each quadrature point for each element and face.

Return type

None

class 3_LESARD.SourceCode._Solver.SpatialSchemes.CG.AssociatedMeshType(SchemeParams=[1])¶

MeshType (string) – the mesh type according to fenics’s classification

MeshOrder (integer) – the mesh order

Note

This is only a product-type class: no method is available

Parameters: SchemeParams (string list, optional) – the parameters of the spatial scheme wished by the user

class 3_LESARD.SourceCode._Solver.SpatialSchemes.CG.Scheme(Problem, Mesh, QuadratureRules, *SchemeParams)¶

Class furnishing all the schemes tools and registers the scheme’s wished parameters. The main iteration is accessible with the method “Iteration”.

Repeats the instance’s initialisation arguments as fields with identical names within the structure. Has for additional field upon instance creation the fields:

Order (integer) – The order of the used basis functions

InnerQBFValues (float numpy array) – Value of the basis function at the quadrature points of each element (NbInnerElementsx NbQuadraturePoints x NbBasisFunc)

InnerQWeigths (float numpy array) – Weights of the quadrature points of each element (NbInnerElements x NbQuadraturePoints)

InnerQGFValues (float numpy array) – Value of the gradient of the basis function at the quadrature points of each element (NbInnerElements x NbQuadraturePoints x NbBasisFunc x dim)

InnerQPoints (float numpy array) – Quadrature points of each element (NbInnerElements x NbQuadraturePoints)

FaceWiseQWeigths (float numpy array) – Weights of the quadrature points of each element’s face (NbInnerElements x NbFace x NbQuadraturePoints)

FaceWiseQPoints (float numpy array) – Quadrature points of each element’s face (NbInnerElements x NbFace x NbQuadraturePoints)

FaceWiseQBFValues (float numpy array) – Value of the basis function at the quadrature points of each element’s face (NbInnerElements x NbFace x NbQuadraturePoints x NbBasisFunc)

Parameters

Problem (Problem) – the considered problem
Mesh (MeshStructure) – the considered mesh instance
QuadratureRules (Quadratures) – the quadratures to use within the scheme.
SchemeParams (string list) – the scheme’s parameters as wished by the user

Methods

ComputeFlux(FlagPoints, U, LSValues)¶

Emulates a flux computation as done in the iteration routine in order to be used in the DeC subtimestep evaluation.

Parameters

FlagPoints (function callback) – mapper to the routine of the FluidSpotter FlagPoints method to flag the Fluid on given points according the given LSValues at Dofs
U (numpy float array) – buffer containing the current state values at each dof (NbVars x NbDofs)
LSValues (numpy float array) – buffer containing the current FluidSpotters values at each dof(NbFluids x NbDofs)

Returns

fluxes in the format required by the Iteration routine

Return type

fluxes (numpy float (multiD)array)

Iteration(FlagPoints, Solution, fluxes, i, du=0, dt=1)¶

Main iteration of the scheme, implementing the most stupid scheme you can think of.

Parameters

FlagPoints (function callback) – the handle of a function flagging the points to the relevant fluid (not used here)
Solution (solution structure) – structure containing the current solution’s values to iterate
fluxes (numpy (multiD)array) – pre-computed fluxes at the points of interest. For this scheme, access with fluxes[element, face, coordinate(fx or fy), variable, pointindex]
i (integer) – the index of the considered element within which the partial residuals will be computed
du (float numpy array) – (optional) when using DeC, the difference in the time iteration
dt (float) – (optional) when using DeC, the full time step

Returns

the computed residuals (NbVars x NbDofs)

Return type

Resu (float numpy array)

ReconstructSolutionAtVertices(Solution)¶

Routine that maps the values from the Dofs to the Physical vertices of the mesh of the solution.

Parameters: Solution (Solution) – the currently being computed solution
Returns: fills direclty the RSol and RFluidFlag values in the data structure
Return type: None

Note

This is only for later plotting purposes.

PreEvaluateQuadratureQuantities()¶

Precomputing and storing the values of the basis functions at the quadrature points of each element

Parameters

None – Considers the given parameters of the class directly

Returns

Creates the fields InnerBFValues and FaceWiseBFValues in the scheme structure, containing: the values of each basis function at each quadrature point for each element and face.

Return type

None

class 3_LESARD.SourceCode._Solver.SpatialSchemes.CG_Primary.AssociatedMeshType(SchemeParams=[1])¶

MeshType (string) – the mesh type according to fenics’s classification

MeshOrder (integer) – the mesh order

Note

This is only a product-type class: no method is available

Parameters: SchemeParams (string list, optional) – the parameters of the spatial scheme wished by the user

class 3_LESARD.SourceCode._Solver.SpatialSchemes.CG_Primary.Scheme(Problem, Mesh, QuadratureRules, *SchemeParams)¶

Class furnishing all the schemes tools and registers the scheme’s wished parameters. The main iteration is accessible with the method “Iteration”.

Repeats the instance’s initialisation arguments as fields with identical names within the structure.Has for additional field upon instance creation the fields:

Order (integer) – The order of the used basis functions

InnerQBFValues (float numpy array) – Value of the basis function at the quadrature points of each element (NbInnerElementsx NbQuadraturePoints x NbBasisFunc)

InnerQWeigths (float numpy array) – Weights of the quadrature points of each element (NbInnerElements x NbQuadraturePoints)

InnerQGFValues (float numpy array) – Value of the gradient of the basis function at the quadrature points of each element (NbInnerElements x NbQuadraturePoints x NbBasisFunc x dim)

InnerQPoints (float numpy array) – Quadrature points of each element (NbInnerElements x NbQuadraturePoints)

FaceWiseQWeigths (float numpy array) – Weights of the quadrature points of each element’s face (NbInnerElements x NbFace x NbQuadraturePoints)

FaceWiseQPoints (float numpy array) – Quadrature points of each element’s face (NbInnerElements x NbFace x NbQuadraturePoints)

FaceWiseQBFValues (float numpy array) – Value of the basis function at the quadrature points of each element’s face (NbInnerElements x NbFace x NbQuadraturePoints x NbBasisFunc)

Note

This scheme is the CG one where the variables interpolated are rho, rhoU,

rhoV, p instead of the conservative ones, in order to preserve the pressure contacts if any

Parameters

Problem (Problem) – the considered problem
Mesh (MeshStructure) – the considered mesh instance
QuadratureRules (Quadratures) – the quadratures to use within the scheme.
SchemeParams (string list) – the scheme’s parameters as wished by the user

Methods

ComputeFlux(FlagPoints, U, LSValues)¶

Emulates a flux computation as done in the iteration routine in order to be used in the DeC subtimestep evaluation.

Parameters

FlagPoints (function callback) – mapper to the routine of the FluidSpotter FlagPoints method to flag the Fluid on given points according the given LSValues at Dofs
U (numpy float array) – buffer containing the current state values at each dof (NbVars x NbDofs)
LSValues (numpy float array) – buffer containing the current FluidSpotters values at each dof(NbFluids x NbDofs)

Returns

fluxes in the format required by the Iteration routine

Return type

fluxes (numpy float (multiD)array)

Iteration(FlagPoints, Solution, fluxes, i, du=0, dt=1)¶

Main iteration of the scheme, implementing the most stupid scheme you can think of.

Parameters

FlagPoints (function callback) – the handle of a function flagging the points to the relevant fluid (not used here)
Solution (solution structure) – structure containing the current solution’s values to iterate
fluxes (numpy (multiD)array) – pre-computed fluxes at the points of interest. For this scheme, access with fluxes[element, face, coordinate(fx or fy), variable, pointindex]
i (integer) – the index of the considered element within which the partial residuals will be computed
du (float numpy array) – (optional) when using DeC, the difference in the time iteration
dt (float) – (optional) when using DeC, the full time step

Returns

the computed residuals (NbVars x NbDofs)

Return type

Resu (float numpy array)

ReconstructSolutionAtVertices(Solution)¶

Routine that maps the values from the Dofs to the Physical vertices of the mesh of the solution.

Parameters: Solution (Solution) – the currently being computed solution
Returns: fills direclty the RSol and RFluidFlag values in the data structure
Return type: None

Note

This is only for later plotting purposes.

PreEvaluateQuadratureQuantities()¶

Precomputing and storing the values of the basis functions at the quadrature points of each element

Parameters

None – Considers the given parameters of the class directly

Returns

Creates the fields InnerBFValues and FaceWiseBFValues in the scheme structure, containing: the values of each basis function at each quadrature point for each element and face.

Return type

None

Spatial Schemes¶

Continuous galerkin + Lax-Friedrichs¶

Continuous galerkin + Lax-Friedrichs ¶