SELF_ECAdvection2D_t Module

  1. SELF_ECAdvection2D_t.f90
  2. SELF_ECAdvection2D_t

Entropy-conserving linear scalar advection equation in 2-D.

Solves: du/dt + u_a * du/dx + v_a * du/dy = 0

Entropy function: eta(u) = u^2 / 2 (same as Trixi.jl)

EC two-point flux (arithmetic mean, entropy-conserving for eta = u^2/2): F^EC(uL, uR) = (u_a * (uL+uR)/2, v_a * (uL+uR)/2)

Surface Riemann flux (Local Lax-Friedrichs / Rusanov): F_Riemann = 0.5 * (a.n) * (uL+uR) - 0.5 * |a| * (uR-uL) where |a| = sqrt(u^2 + v^2) is the maximum wave speed. This is dissipative (entropy-stable) and reduces to the central flux when uL = uR (no dissipation at no-normal-flow or mirror boundaries).


Uses

  • module~~self_ecadvection2d_t~~UsesGraph module~self_ecadvection2d_t SELF_ECAdvection2D_t module~self_ecdgmodel2d_t SELF_ECDGModel2D_t module~self_ecadvection2d_t->module~self_ecdgmodel2d_t module~self_mesh SELF_Mesh module~self_ecadvection2d_t->module~self_mesh module~self_boundaryconditions SELF_BoundaryConditions module~self_ecadvection2d_t->module~self_boundaryconditions module~self_dgmodel2d_t SELF_DGModel2D_t module~self_ecdgmodel2d_t->module~self_dgmodel2d_t module~self_mappedtwopointvector_2d~2 SELF_MappedTwoPointVector_2D module~self_ecdgmodel2d_t->module~self_mappedtwopointvector_2d~2 module~self_constants SELF_Constants module~self_mesh->module~self_constants module~self_domaindecomposition~2 SELF_DomainDecomposition module~self_mesh->module~self_domaindecomposition~2 iso_c_binding iso_c_binding module~self_mesh->iso_c_binding module~self_metadata SELF_Metadata module~self_boundaryconditions->module~self_metadata module~self_supportroutines SELF_SupportRoutines module~self_boundaryconditions->module~self_supportroutines module~self_boundaryconditions->iso_c_binding module~self_dgmodel2d_t->module~self_boundaryconditions module~self_dgmodel2d_t->module~self_metadata module~self_dgmodel2d_t->module~self_supportroutines module~self_hdf5 SELF_HDF5 module~self_dgmodel2d_t->module~self_hdf5 module~self_mappedscalar_2d SELF_MappedScalar_2D module~self_dgmodel2d_t->module~self_mappedscalar_2d module~self_model SELF_Model module~self_dgmodel2d_t->module~self_model module~self_geometry_2d SELF_Geometry_2D module~self_dgmodel2d_t->module~self_geometry_2d HDF5 HDF5 module~self_dgmodel2d_t->HDF5 module~self_mappedvector_2d SELF_MappedVector_2D module~self_dgmodel2d_t->module~self_mappedvector_2d module~self_mesh_2d~2 SELF_Mesh_2D module~self_dgmodel2d_t->module~self_mesh_2d~2 FEQParse FEQParse module~self_dgmodel2d_t->FEQParse module~self_mappedtwopointvector_2d_t SELF_MappedTwoPointVector_2D_t module~self_mappedtwopointvector_2d~2->module~self_mappedtwopointvector_2d_t module~self_constants->iso_c_binding iso_fortran_env iso_fortran_env module~self_constants->iso_fortran_env module~self_metadata->module~self_hdf5 module~self_metadata->HDF5 module~self_supportroutines->module~self_constants module~self_supportroutines->iso_fortran_env module~self_domaindecomposition_t SELF_DomainDecomposition_t module~self_domaindecomposition~2->module~self_domaindecomposition_t module~self_hdf5->module~self_constants module~self_hdf5->HDF5 module~self_hdf5->iso_fortran_env mpi mpi module~self_hdf5->mpi module~self_mappedscalar_2d_t SELF_MappedScalar_2D_t module~self_mappedscalar_2d->module~self_mappedscalar_2d_t module~self_model->module~self_metadata module~self_model->module~self_supportroutines module~self_model->module~self_hdf5 module~self_model->HDF5 module~self_model->FEQParse module~self_domaindecomposition_t->module~self_constants module~self_domaindecomposition_t->module~self_supportroutines module~self_domaindecomposition_t->iso_c_binding module~self_domaindecomposition_t->mpi module~self_lagrange~3 SELF_Lagrange module~self_domaindecomposition_t->module~self_lagrange~3 module~self_geometry_2d->module~self_constants module~self_geometry_2d->module~self_supportroutines module~self_geometry_2d->module~self_mesh_2d~2 module~self_scalar_2d~2 SELF_Scalar_2D module~self_geometry_2d->module~self_scalar_2d~2 module~self_data SELF_Data module~self_geometry_2d->module~self_data module~self_geometry_2d->module~self_lagrange~3 module~self_vector_2d~2 SELF_Vector_2D module~self_geometry_2d->module~self_vector_2d~2 module~self_tensor_2d~2 SELF_Tensor_2D module~self_geometry_2d->module~self_tensor_2d~2 module~self_mappedvector_2d_t SELF_MappedVector_2D_t module~self_mappedvector_2d->module~self_mappedvector_2d_t module~self_mesh_2d_t SELF_Mesh_2D_t module~self_mesh_2d~2->module~self_mesh_2d_t module~self_mappedtwopointvector_2d_t->module~self_constants module~self_mappedtwopointvector_2d_t->iso_c_binding module~self_mappedtwopointvector_2d_t->module~self_geometry_2d module~self_twopointvector_2d~2 SELF_TwoPointVector_2D module~self_mappedtwopointvector_2d_t->module~self_twopointvector_2d~2 module~self_mappedtwopointvector_2d_t->module~self_lagrange~3 module~self_scalar_2d~2->module~self_constants module~self_scalar_2d~2->iso_c_binding module~self_scalar_2d_t SELF_Scalar_2D_t module~self_scalar_2d~2->module~self_scalar_2d_t module~self_data->module~self_constants module~self_data->module~self_metadata module~self_data->iso_c_binding module~self_data->module~self_hdf5 module~self_data->HDF5 module~self_data->FEQParse module~self_data->module~self_lagrange~3 module~self_mappedvector_2d_t->module~self_constants module~self_mappedvector_2d_t->module~self_domaindecomposition~2 module~self_mappedvector_2d_t->iso_c_binding module~self_mappedvector_2d_t->module~self_geometry_2d module~self_mappedvector_2d_t->module~self_mesh_2d~2 module~self_mappedvector_2d_t->FEQParse module~self_mappedvector_2d_t->module~self_lagrange~3 module~self_mappedvector_2d_t->module~self_vector_2d~2 module~self_mappedvector_2d_t->module~self_tensor_2d~2 module~self_mesh_2d_t->module~self_mesh module~self_mesh_2d_t->module~self_constants module~self_mesh_2d_t->module~self_supportroutines module~self_mesh_2d_t->module~self_domaindecomposition~2 module~self_mesh_2d_t->iso_c_binding module~self_mesh_2d_t->module~self_hdf5 module~self_mesh_2d_t->HDF5 module~self_mesh_2d_t->module~self_lagrange~3 module~self_twopointvector_2d_t SELF_TwoPointVector_2D_t module~self_twopointvector_2d~2->module~self_twopointvector_2d_t module~self_mappedscalar_2d_t->module~self_constants module~self_mappedscalar_2d_t->module~self_domaindecomposition~2 module~self_mappedscalar_2d_t->iso_c_binding module~self_mappedscalar_2d_t->module~self_geometry_2d module~self_mappedscalar_2d_t->module~self_mesh_2d~2 module~self_mappedscalar_2d_t->FEQParse module~self_mappedscalar_2d_t->module~self_scalar_2d~2 module~self_mappedscalar_2d_t->module~self_lagrange~3 module~self_mappedscalar_2d_t->module~self_tensor_2d~2 module~self_lagrange~3->module~self_constants module~self_lagrange~3->iso_c_binding module~self_lagrange~3->iso_fortran_env module~self_lagrange_t SELF_Lagrange_t module~self_lagrange~3->module~self_lagrange_t module~self_vector_2d_t SELF_Vector_2D_t module~self_vector_2d~2->module~self_vector_2d_t module~self_tensor_2d_t SELF_Tensor_2D_t module~self_tensor_2d~2->module~self_tensor_2d_t module~self_vector_2d_t->module~self_constants module~self_vector_2d_t->module~self_metadata module~self_vector_2d_t->iso_c_binding module~self_vector_2d_t->module~self_hdf5 module~self_vector_2d_t->HDF5 module~self_vector_2d_t->FEQParse module~self_vector_2d_t->module~self_data module~self_vector_2d_t->module~self_lagrange~3 module~self_lagrange_t->module~self_constants module~self_lagrange_t->module~self_supportroutines module~self_lagrange_t->iso_c_binding module~self_lagrange_t->module~self_hdf5 module~self_lagrange_t->HDF5 module~self_lagrange_t->iso_fortran_env module~self_quadrature SELF_Quadrature module~self_lagrange_t->module~self_quadrature module~self_tensor_2d_t->module~self_constants module~self_tensor_2d_t->module~self_metadata module~self_tensor_2d_t->iso_c_binding module~self_tensor_2d_t->module~self_hdf5 module~self_tensor_2d_t->HDF5 module~self_tensor_2d_t->FEQParse module~self_tensor_2d_t->module~self_data module~self_tensor_2d_t->module~self_lagrange~3 module~self_scalar_2d_t->module~self_constants module~self_scalar_2d_t->module~self_metadata module~self_scalar_2d_t->iso_c_binding module~self_scalar_2d_t->module~self_hdf5 module~self_scalar_2d_t->HDF5 module~self_scalar_2d_t->FEQParse module~self_scalar_2d_t->module~self_data module~self_scalar_2d_t->module~self_lagrange~3 module~self_twopointvector_2d_t->module~self_constants module~self_twopointvector_2d_t->module~self_metadata module~self_twopointvector_2d_t->iso_c_binding module~self_twopointvector_2d_t->FEQParse module~self_twopointvector_2d_t->module~self_data module~self_twopointvector_2d_t->module~self_lagrange~3 module~self_quadrature->module~self_constants module~self_quadrature->iso_fortran_env

Used by

  • module~~self_ecadvection2d_t~~UsedByGraph module~self_ecadvection2d_t SELF_ECAdvection2D_t module~self_ecadvection2d SELF_ECAdvection2D module~self_ecadvection2d->module~self_ecadvection2d_t module~self_ecadvection2d~2 SELF_ECAdvection2D module~self_ecadvection2d~2->module~self_ecadvection2d_t

Contents

Derived Types

Functions

Subroutines


Derived Types

type, public, extends(ECDGModel2D_t) :: ECAdvection2D_t

Components

TypeVisibilityAttributesNameInitial
type(MappedScalar2D), public :: dSdt
real(kind=prec), public :: dt
real(kind=prec), public :: entropy
type(MappedVector2D), public :: flux
type(MappedScalar2D), public :: fluxDivergence
type(SEMQuad), public, pointer:: geometry
logical, public :: gradient_enabled =.false.
type(BoundaryConditionList), public :: hyperbolicBCs
integer, public :: ioIterate =0
type(Mesh2D), public, pointer:: mesh
integer, public :: nvar
type(BoundaryConditionList), public :: parabolicBCs
logical, public :: prescribed_bcs_enabled =.true.
type(MappedScalar2D), public :: solution
type(MappedVector2D), public :: solutionGradient
type(MappedScalar2D), public :: source
real(kind=prec), public :: t
logical, public :: tecplot_enabled =.true.
procedure(SELF_timeIntegrator), public, pointer:: timeIntegrator=> Euler_timeIntegrator
type(MappedTwoPointVector2D), public :: twoPointFlux
real(kind=prec), public :: u
real(kind=prec), public :: v
type(MappedScalar2D), public :: workSol

Type-Bound Procedures

procedure, public :: AdditionalFree => AdditionalFree_Model
procedure, public :: AdditionalInit => AdditionalInit_ECAdvection2D_t
procedure, public :: AdditionalOutput => AdditionalOutput_Model
procedure, public :: BoundaryFlux => BoundaryFlux_DGModel2D_t
procedure, public :: CalculateEntropy => CalculateEntropy_DGModel2D_t
procedure, public :: CalculateSolutionGradient => CalculateSolutionGradient_DGModel2D_t
procedure, public :: CalculateTendency => CalculateTendency_ECDGModel2D_t
procedure, public :: Euler_timeIntegrator
procedure, public :: FluxMethod => fluxmethod_DGModel2D_t
procedure, public :: ForwardStep => ForwardStep_Model
procedure, public :: Free => Free_ECDGModel2D_t
procedure, public :: GetSimulationTime
procedure, public :: IncrementIOCounter
procedure, public :: Init => Init_ECDGModel2D_t
procedure, public :: LowStorageRK2_timeIntegrator
procedure, public :: LowStorageRK3_timeIntegrator
procedure, public :: LowStorageRK4_timeIntegrator
procedure, public :: MapBoundaryConditions => MapBoundaryConditions_DGModel2D_t
procedure, public :: PreTendency => PreTendency_Model
procedure, public :: PrintType => PrintType_Model
procedure, public :: ReadModel => Read_DGModel2D_t
procedure, public :: ReportEntropy => ReportEntropy_Model
procedure, public :: ReportMetrics => ReportMetrics_DGModel2D_t
procedure, public :: ReportUserMetrics => ReportUserMetrics_Model
procedure, public :: SetBoundaryCondition => setboundarycondition_DGModel2D_t
procedure, public :: SetGradientBoundaryCondition => setgradientboundarycondition_DGModel2D_t
procedure, public :: SetMetadata => SetMetadata_DGModel2D_t
procedure, public :: SetNumberOfVariables => SetNumberOfVariables_Model
procedure, public :: SetSimulationTime
generic, public :: SetSolution => SetSolutionFromChar_DGModel2D_t, SetSolutionFromEqn_DGModel2D_t
generic, public :: SetTimeIntegrator => SetTimeIntegrator_withChar
procedure, public :: SourceMethod => sourcemethod_DGModel2D_t
procedure, public :: TwoPointFluxMethod => TwoPointFluxMethod_ECDGModel2D_t
procedure, public :: UpdateGRK2 => UpdateGRK2_DGModel2D_t
procedure, public :: UpdateGRK3 => UpdateGRK3_DGModel2D_t
procedure, public :: UpdateGRK4 => UpdateGRK4_DGModel2D_t
procedure, public :: UpdateSolution => UpdateSolution_DGModel2D_t
procedure, public :: WriteModel => Write_DGModel2D_t
procedure, public :: WriteTecplot => WriteTecplot_DGModel2D_t
procedure, public :: entropy_func => entropy_func_ECAdvection2D_t
procedure, public :: flux1D => flux1d_Model
procedure, public :: flux2D => flux2d_Model
procedure, public :: flux3D => flux3d_Model
procedure, public :: riemannflux1d => riemannflux1d_Model
procedure, public :: riemannflux2d => riemannflux2d_ECAdvection2D_t
procedure, public :: riemannflux3d => riemannflux3d_Model
procedure, public :: source1d => source1d_Model
procedure, public :: source2d => source2d_Model
procedure, public :: source3d => source3d_Model
procedure, public :: twopointflux2d => twopointflux2d_ECAdvection2D_t

Functions

public pure function entropy_func_ECAdvection2D_t(this, s) result(e)

Quadratic entropy: eta(u) = u^2 / 2

Arguments

TypeIntentOptionalAttributesName
class(ECAdvection2D_t), intent(in) :: this
real(kind=prec), intent(in) :: s(1:this%nvar)

Return Value real(kind=prec)

public pure function riemannflux2d_ECAdvection2D_t(this, sL, sR, dsdx, nhat) result(flux)

Local Lax-Friedrichs (Rusanov) Riemann flux for linear advection. Entropy-stable: provides symmetric dissipation at element interfaces. lambda_max = sqrt(u^2 + v^2) is the maximum wave speed.

Arguments

TypeIntentOptionalAttributesName
class(ECAdvection2D_t), intent(in) :: this
real(kind=prec), intent(in) :: sL(1:this%nvar)
real(kind=prec), intent(in) :: sR(1:this%nvar)
real(kind=prec), intent(in) :: dsdx(1:this%nvar,1:2)
real(kind=prec), intent(in) :: nhat(1:2)

Return Value real(kind=prec)(1:this%nvar)

public pure function twopointflux2d_ECAdvection2D_t(this, sL, sR) result(flux)

Arithmetic-mean two-point flux for linear advection. Entropy-conserving with respect to eta(u) = u^2/2.

Arguments

TypeIntentOptionalAttributesName
class(ECAdvection2D_t), intent(in) :: this
real(kind=prec), intent(in) :: sL(1:this%nvar)
real(kind=prec), intent(in) :: sR(1:this%nvar)

Return Value real(kind=prec)(1:this%nvar,1:2)


Subroutines

public subroutine AdditionalInit_ECAdvection2D_t(this)

Arguments

TypeIntentOptionalAttributesName
class(ECAdvection2D_t), intent(inout) :: this

public subroutine hbc2d_NoNormalFlow_ECAdvection2D(bc, mymodel)

Mirror boundary condition: sets extBoundary = interior state. With the LLF Riemann flux, this gives sR = sL at the boundary, so the Riemann flux reduces to the central flux (a.n)*s — no dissipation. Use this BC when testing entropy conservation.

Arguments

TypeIntentOptionalAttributesName
class(BoundaryCondition), intent(in) :: bc
class(Model), intent(inout) :: mymodel