atl_modg_2d_kernel_module Module

Module for routines and datatypes of MOdal Discontinuous Galerkin (MODG) scheme. This scheme is a spectral scheme for linear, purley hyperbolic partial differential equation systems.

Todo

HK: Split this module into three: a common one, a Q part and a P part.


Uses

Used by

  • module~~atl_modg_2d_kernel_module~~UsedByGraph module~atl_modg_2d_kernel_module atl_modg_2d_kernel_module module~atl_container_module atl_container_module module~atl_container_module->module~atl_modg_2d_kernel_module proc~compute_rhs_cubes_modg_2d compute_rhs_cubes_modg_2d proc~compute_rhs_cubes_modg_2d->module~atl_modg_2d_kernel_module proc~postprocess_rhs_cubes postprocess_rhs_cubes proc~postprocess_rhs_cubes->module~atl_modg_2d_kernel_module proc~preprocess_rhs_cubes preprocess_rhs_cubes proc~preprocess_rhs_cubes->module~atl_modg_2d_kernel_module module~atl_initialize_module atl_initialize_module module~atl_initialize_module->module~atl_container_module module~atl_program_module atl_program_module module~atl_program_module->module~atl_container_module module~atl_program_module->module~atl_initialize_module program~ateles ateles program~ateles->module~atl_container_module program~ateles->module~atl_program_module program~atl_harvesting atl_harvesting program~atl_harvesting->module~atl_container_module program~atl_harvesting->module~atl_initialize_module program~atl_harvesting->module~atl_program_module

Subroutines

public subroutine atl_init_modg_2d_kernel(kerneldata_list, statedata_list, statedata_stab_list, mesh_list, scheme_list, boundary_list, boundary_stab_list, equation, tree, time, commPattern, need_deviation)

Initiate the MODG kernel for cubic elements on all levels.

Arguments

Type IntentOptional Attributes Name
type(atl_kerneldata_type), allocatable :: kerneldata_list(:)

Array of kerneldata_types, one for each level. They will be initialized.
type(atl_statedata_type), allocatable :: statedata_list(:)

Array of statedata_types, one for each level.
type(atl_statedata_type), allocatable :: statedata_stab_list(:,:)
type(atl_cube_elem_type), allocatable :: mesh_list(:)

List of cubic meshes. One entry per level.
type(atl_scheme_type), allocatable :: scheme_list(:)

List of schemes on the levels.
type(atl_level_boundary_type), allocatable :: boundary_list(:)

The boundary description for the faces on the current level.
type(atl_level_boundary_type), allocatable :: boundary_stab_list(:)

The boundary description for the faces on the current level.
type(atl_Equations_type) :: equation

The equation type.
type(treelmesh_type), intent(in) :: tree

The tree of the simulation domain
type(tem_time_type), intent(in) :: time

current time
type(tem_commPattern_type), intent(in) :: commPattern

mpi communication pattern type
logical, intent(in) :: need_deviation

Flag to indicate whether maximal polynomial deviations should be computed for the state.

public subroutine atl_preprocess_modg_2d_kernel(currentLevel, minLevel, maxLevel, equation, statedata, mesh_list, boundary_list, scheme_list, poly_proj_material, material_list, commPattern, proc)

Subroutine to execute the preprocessing for the MODG kernels. Currently this includes: Convert external source terms to modal representation.

Arguments

Type IntentOptional Attributes Name
integer, intent(in) :: currentLevel
integer, intent(in) :: minLevel
integer, intent(in) :: maxLevel
type(atl_Equations_type), intent(inout) :: equation
type(atl_statedata_type), intent(inout) :: statedata
type(atl_cube_elem_type), intent(inout) :: mesh_list(minlevel:maxlevel)
type(atl_level_boundary_type), intent(in) :: boundary_list(minlevel:maxLevel)
type(atl_scheme_type), intent(inout) :: scheme_list(minlevel:maxlevel)
type(ply_poly_project_type), intent(inout) :: poly_proj_material
type(atl_material_type), intent(inout) :: material_list(minlevel:maxlevel)
type(tem_commPattern_type) :: commPattern

mpi communication pattern type
type(tem_comm_env_type) :: proc

mpi communication environment with mpi communicator

public subroutine atl_modg_2d_project_NumFlux(mesh, equation, kerneldata, facedata, penalizationdata, usePenalization, scheme, poly_proj, dl_prod, dl_prodDiff)

Subroutine to project modal representations of numerical flux and source terms onto test functions.

Arguments

Type IntentOptional Attributes Name
type(atl_cube_elem_type), intent(in) :: mesh

Descritption of the cubical elements in the mesh
type(atl_Equations_type), intent(in) :: equation

The equation description.
type(atl_kerneldata_type), intent(inout) :: kerneldata

The data of the kernel. Holds the physical fluxes.
type(atl_facedata_type), intent(inout) :: facedata

The representation on the face + representation of the flux.
type(atl_penalizationData_type), intent(in) :: penalizationdata

Volumetric data for the penalization
logical, intent(in) :: usePenalization

Flag to indicate whether the penalization data has to be considered, or if it is taken care of somewhere else (imex)
type(atl_modg_2d_scheme_type), intent(in) :: scheme

The parameters of the MODG scheme
type(ply_poly_project_type), intent(inout) :: poly_proj

Projection for the current level
real(kind=rk), intent(in) :: dl_prod(2,scheme%maxPolyDegree+1)

Precomputed scalar products of the test and ansatz function
real(kind=rk), intent(in) :: dl_prodDiff(2,scheme%maxPolyDegree+1)

public subroutine atl_modg_2d_project_source(sourcedata, nScalars, mesh, scheme, kerneldata, currentLevel)

Projection of the source terms (in modal representation) to the test functions.

Arguments

Type IntentOptional Attributes Name
type(atl_source_type), intent(in) :: sourcedata

The modal representation of the source
integer, intent(in) :: nScalars

The number scalar variables in the equation system.
type(atl_cube_elem_type), intent(in) :: mesh

The cubical elements.
type(atl_modg_2d_scheme_type), intent(in) :: scheme

The parameters of the MODG scheme
type(atl_kerneldata_type), intent(inout) :: kerneldata

The data of the kernel. This one is updated by the projection.
integer, intent(in) :: currentLevel

The current level

public subroutine atl_modg_2d_modalVolToModalFace(mesh, statedata, facedata, equation, modg_2d)

Projects modal representation of each cell to its faces, i.e. this subroutine creates a modal representation on the faces.

Arguments

Type IntentOptional Attributes Name
type(atl_cube_elem_type), intent(in) :: mesh

The elements we apply the projection for.
type(atl_statedata_type), intent(in) :: statedata

Volumetric, modal states for each element.
type(atl_facedata_type), intent(inout) :: facedata

Modal representation on the face (will be updated by this routine for all fluid elements in mesh).
type(atl_Equations_type), intent(in) :: equation

The equation system under consideration
type(atl_modg_2d_scheme_type), intent(in) :: modg_2d

The parameters of your modg scheme.

public subroutine atl_modg_2d_ensure_pos_facemean(nElems_fluid, volState, faceRep, nScalars, ensure_positivity)

Lift the mean on the face to a positive value if necessary.

Read more…

Arguments

Type IntentOptional Attributes Name
integer, intent(in) :: nElems_fluid

Number of fluid elements
real(kind=rk), intent(in) :: volState(:,:,:)

Volumetric modal states for each element
type(atl_faceRep_type), intent(inout) :: faceRep(:)

Modal representation on the face that might need limiting.

Read more…
integer, intent(in) :: nScalars

Number of variables
logical, intent(in) :: ensure_positivity(:)

Indication for each variable, whether positivity is to be ensured or not.

Read more…

public subroutine atl_modg_2d_invMassMatrix(mesh, equation, kerneldata, statedata, elementalTimestep, timestep, scheme)

Applies the inverse of the mass matrix for a 2D scheme.

Arguments

Type IntentOptional Attributes Name
type(atl_cube_elem_type) :: mesh

The mesh you are working with.
type(atl_Equations_type) :: equation

The equation you solve.
type(atl_kerneldata_type) :: kerneldata

The data of the kernel.
type(atl_statedata_type) :: statedata

THe state if the equation
procedure(atl_elemental_timestep_vec), intent(in), pointer :: elementalTimestep

The elemental timestepping routine, because of performance, this is constant.
type(atl_timestep_type) :: timestep

The timestepping data.
type(atl_modg_2d_scheme_type), intent(in) :: scheme

Parameters of the modal dg scheme

private subroutine modg_2d_project_penalization_Q(nScalars, mesh, maxPolyDegree, kerneldata, penalizationdata)

Projection of the penalization terms (in modal representation) to the test functions.

Arguments

Type IntentOptional Attributes Name
integer, intent(in) :: nScalars

The number scalar variables in the equation system.
type(atl_cube_elem_type), intent(in) :: mesh

The cubical elements.
integer, intent(in) :: maxPolyDegree

The maximal polynomial degree of the modg scheme
type(atl_kerneldata_type), intent(inout) :: kerneldata

The data of the kernel. This one is updated by the projection.
type(atl_penalizationData_type), intent(in) :: penalizationdata

Volumetric data for the penalization

private subroutine modg_2d_project_source_Q(nScalars, sourcedata, maxPolyDegree, mesh, kerneldata, currentLevel)

Projection of the source terms (in modal representation) to the test functions.

Arguments

Type IntentOptional Attributes Name
integer, intent(in) :: nScalars

The number scalar variables in the equation system.
type(atl_source_type), intent(in) :: sourcedata

The modal representation of the source
integer, intent(in) :: maxPolyDegree

The maximal polynomial degree of the modg scheme
type(atl_cube_elem_type), intent(in) :: mesh

The cubical elements.
type(atl_kerneldata_type), intent(inout) :: kerneldata

The data of the kernel. This one is updated by the projection.
integer, intent(in) :: currentLevel

The current level

private subroutine modg_2d_project_source_P(nScalars, sourcedata, maxPolyDegree, mesh, kerneldata, currentLevel)

Projection of the source terms (in modal representation) to the test functions.

Arguments

Type IntentOptional Attributes Name
integer, intent(in) :: nScalars

The number scalar variables in the equation system.
type(atl_source_type), intent(in) :: sourcedata

The modal representation of the source
integer, intent(in) :: maxPolyDegree

The maximal polynomial degree of the modg scheme
type(atl_cube_elem_type), intent(in) :: mesh

The cubical elements.
type(atl_kerneldata_type), intent(inout) :: kerneldata

The data of the kernel. This one is updated by the projection.
integer, intent(in) :: currentLevel

The current level

private subroutine modg_2d_project_stabViscNumFluxX_Q(numFlux, faceState, equation, maxPolyDegree, length, nElems_fluid, projection, poly_proj)

Projection of the numerical flux in x direction onto the testfunctions.

Arguments

Type IntentOptional Attributes Name
real(kind=rk), intent(inout) :: numFlux(:,:,:,:)

The numerical flux on the faces in modal representations. Dimension is (maxPolyDegree+1)^2 , nScalars
real(kind=rk), intent(inout) :: faceState(:,:,:,:)

The state on the faces in modal representations. Dimension is (maxPolyDegree+1)^2 , nScalars
type(atl_Equations_type), intent(in) :: equation

The equation system under consideration
integer, intent(in) :: maxPolyDegree

The maximal polynomial degree in each spatial direction.
real(kind=rk), intent(in) :: length

The length of the cubes.
integer, intent(in) :: nElems_fluid

The element index
real(kind=rk), intent(inout) :: projection(:,:,:)

The numerical flux projected onto the test functions.
type(ply_poly_project_type), intent(inout) :: poly_proj

Projection for the current level

private subroutine modg_2d_project_stabViscNumFluxY_Q(numFlux, faceState, equation, maxPolyDegree, length, nElems_fluid, projection, poly_proj)

Projection of the numerical flux in y direction onto the testfunctions.

Arguments

Type IntentOptional Attributes Name
real(kind=rk), intent(inout) :: numFlux(:,:,:,:)

The numerical flux on the faces in modal representations. Dimension is (maxPolyDegree+1)^2 , nScalars
real(kind=rk), intent(inout) :: faceState(:,:,:,:)

The state on the faces in modal representations. Dimension is (maxPolyDegree+1)^2 , nScalars
type(atl_Equations_type), intent(in) :: equation

The equation system under consideration
integer, intent(in) :: maxPolyDegree

The maximal polynomial degree in each spatial direction.
real(kind=rk), intent(in) :: length

The length of the cubes.
integer, intent(in) :: nElems_fluid

The element index
real(kind=rk), intent(inout) :: projection(:,:,:)

The numerical flux projected onto the test functions.
type(ply_poly_project_type), intent(inout) :: poly_proj

Projection for the current level

private subroutine modg_2d_project_numFluxX_Q(numFlux, nScalars, maxPolyDegree, length, nElems_fluid, dl_prod, projection)

Projection of the numerical flux in x direction onto the testfunctions for Q_space.

Arguments

Type IntentOptional Attributes Name
real(kind=rk), intent(inout) :: numFlux(:,:,:,:)

The numerical flux on the faces in modal representations. Dimension is (maxPolyDegree+1)^2 , nScalars
integer, intent(in) :: nScalars

The number of scalar variables in your equation system.
integer, intent(in) :: maxPolyDegree

The maximal polynomial degree in each spatial direction.
real(kind=rk), intent(in) :: length

The length of the cubes.
integer, intent(in) :: nElems_fluid

The element index
real(kind=rk), intent(in) :: dl_prod(2,maxPolyDegree+1)

Precomputed dual Legendre products:
real(kind=rk), intent(inout) :: projection(:,:,:)

The numerical flux projected onto the test functions.

private subroutine modg_2d_project_numFluxX_diffTestX_Q(numFluxLeftFace, numFluxRightFace, nScalars, maxPolyDegree, length, nElems_fluid, dl_prod, projection)

Projection of the numerical flux in x direction onto the testfunctions.

Arguments

Type IntentOptional Attributes Name
real(kind=rk), intent(inout) :: numFluxLeftFace(:,:,:,:)

The numerical flux on the left face in modal representations. Dimension is (maxPolyDegree+1)^2 , nScalars
real(kind=rk), intent(inout) :: numFluxRightFace(:,:,:,:)

The numerical flux on the right face in modal representations. Dimension is (maxPolyDegree+1)^2 , nScalars
integer, intent(in) :: nScalars

The number of scalar variables in your equation system.
integer, intent(in) :: maxPolyDegree

The maximal polynomial degree in each spatial direction.
real(kind=rk), intent(in) :: length

The length of the cubes.
integer, intent(in) :: nElems_fluid

The element index
real(kind=rk), intent(in) :: dl_prod(2,maxPolyDegree+1)

Precomputed dual Legendre products:
real(kind=rk), intent(inout) :: projection(:,:,:)

The numerical flux projected onto the test functions.

private subroutine modg_2d_project_numFluxY_Q(numFlux, nScalars, maxPolyDegree, length, nElems_fluid, dl_prod, projection)

Projection of the numerical flux in y direction onto the testfunctions for Q_space.

Arguments

Type IntentOptional Attributes Name
real(kind=rk), intent(inout) :: numFlux(:,:,:,:)

The numerical flux on the faces in modal representations. Dimension is (maxPolyDegree+1)^2 , nScalars
integer, intent(in) :: nScalars

The number of scalar variables in your equation system.
integer, intent(in) :: maxPolyDegree

The maximal polynomial degree in each spatial direction.
real(kind=rk), intent(in) :: length

The length of the cubes.
integer, intent(in) :: nElems_fluid

The element index
real(kind=rk), intent(in) :: dl_prod(2,maxPolyDegree+1)

Precomputed dual Legendre products:
real(kind=rk), intent(inout) :: projection(:,:,:)

The numerical flux projected onto the test functions.

private subroutine modg_2d_project_numFluxY_diffTestY_Q(numFluxLeftFace, numFluxRightFace, nScalars, maxPolyDegree, length, nElems_fluid, dl_prod, projection)

Projection of the numerical flux in y direction onto the testfunctions.

Arguments

Type IntentOptional Attributes Name
real(kind=rk), intent(inout) :: numFluxLeftFace(:,:,:,:)

The numerical flux on the left face in modal representations. Dimension is (maxPolyDegree+1)^2 , nScalars
real(kind=rk), intent(inout) :: numFluxRightFace(:,:,:,:)

The numerical flux on the right face in modal representations. Dimension is (maxPolyDegree+1)^2 , nScalars
integer, intent(in) :: nScalars

The number of scalar variables in your equation system.
integer, intent(in) :: maxPolyDegree

The maximal polynomial degree in each spatial direction.
real(kind=rk), intent(in) :: length

The length of the cubes.
integer, intent(in) :: nElems_fluid

The element index
real(kind=rk), intent(in) :: dl_prod(2,maxPolyDegree+1)

Precomputed dual Legendre products:
real(kind=rk), intent(inout) :: projection(:,:,:)

The numerical flux projected onto the test functions.

private subroutine modg_2d_invMassMatrix_Q(mesh, equation, kerneldata, scheme, nElems)

Applies the inverse of the mass matrix for a 2D scheme in Q_space.

Arguments

Type IntentOptional Attributes Name
type(atl_cube_elem_type) :: mesh

The mesh you are working with.
type(atl_Equations_type) :: equation

The equation you solve.
type(atl_kerneldata_type) :: kerneldata

The data of the kernel.
type(atl_modg_2d_scheme_type), intent(in) :: scheme

Parameters of the modal dg scheme
integer, intent(in) :: nElems

private subroutine modg_2d_invMassMatrix_P(mesh, kerneldata, scheme, nElems)

Applies the inverse of the mass matrix for a 2D scheme in P_space.

Arguments

Type IntentOptional Attributes Name
type(atl_cube_elem_type) :: mesh

The mesh you are working with.
type(atl_kerneldata_type) :: kerneldata

The data of the kernel.
type(atl_modg_2d_scheme_type), intent(in) :: scheme

Parameters of the modal dg scheme
integer, intent(in) :: nElems