atl_rktaylor_module Module

Routines,functions, datatypes related to Runge Kutta Taylor methods for arbitrary high order time stepping.

Implementation is based on: Claudio G Canuto and M. Yousuff Hussaini and Alfio Quarteroni and Thomas A. Zang 2nd Edition, page 534, equation D.2.18, section D.2.5 Runge-Kutta Methods ATTENTION: In case that the right hand side of the PDE does not contain any explicit temporal dependence the method is high order accurate, i.e. s-stages yield a RK method of order s.


Uses

Used by

  • module~~atl_rktaylor_module~~UsedByGraph module~atl_rktaylor_module atl_rktaylor_module module~atl_global_time_integration_module atl_global_time_integration_module module~atl_global_time_integration_module->module~atl_rktaylor_module module~atl_container_module atl_container_module module~atl_container_module->module~atl_global_time_integration_module module~atl_program_module atl_program_module module~atl_program_module->module~atl_global_time_integration_module module~atl_program_module->module~atl_container_module module~atl_initialize_module atl_initialize_module module~atl_program_module->module~atl_initialize_module module~atl_initialize_module->module~atl_container_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_program_module program~atl_harvesting->module~atl_initialize_module

Subroutines

public subroutine atl_init_explicitRungeKuttaTaylor(me, minLevel, maxLevel, steps, statedata_list)

Routine to initialize explicit runge kutta taylor scheme for timestepping.

Arguments

Type IntentOptional Attributes Name
type(atl_global_timestep_type), intent(inout) :: me

The datatype to initialize.
integer, intent(in) :: minLevel

The minimum of level of the mesh.
integer, intent(in) :: maxLevel

The maximum of level of the mesh.
integer, intent(in) :: steps

The number of steps in the runge kutta procedure
type(atl_statedata_type), intent(in) :: statedata_list(minLevel:maxLevel)

The state list used in your solver, for each level one entry.

private subroutine update_timestep_rktaylor(me, timestepInfo)

Levelwise updating of runge kutta taylor method

Arguments

Type IntentOptional Attributes Name
class(atl_timestep_type), intent(inout) :: me

The type of your timestepping.
type(atl_local_timestep_type), intent(in) :: timestepInfo

Local timestepping information for that part of the mesh

private subroutine elemental_timestep_rktaylor(me, state, cell, dof, sideFlux)

Elemental operation for timestepping of type Runge Kutta Taylor

Arguments

Type IntentOptional Attributes Name
class(atl_timestep_type), intent(inout) :: me

Description of the timestep integration method.
real(kind=rk), intent(inout) :: state(:,:,:)

The state of all cells on this level. This field will be updated ad the cell position. See kerneldata type for more explanations.
integer, intent(in) :: cell

Position of the cell to update in the state vector.
integer, intent(in) :: dof

The degree of freedom to update
real(kind=rk), intent(in) :: sideFlux(:)

The flux for one of the sides of this cell. The length of this array is the number of conservative variables of your equation.

private subroutine elemental_timestep_vec_rktaylor(me, state, kerneldata)

Elemental operation for timestepping of type Runge Kutta Taylor

Arguments

Type IntentOptional Attributes Name
class(atl_timestep_type), intent(inout) :: me

Description of the timestep integration method.
real(kind=rk), intent(inout) :: state(:,:,:)

The state of all cells on this level. This field will be updated ad the cell position. See kerneldata type for more explanations.
type(atl_kerneldata_type), intent(in) :: kerneldata

Complete kerneldata to get the flux from with additional information.

private subroutine mesh_timestep_rktaylor(minLevel, maxLevel, currentLevel, cubes, tree, timestep_list, nSteps, equation, general, commStateTimer, poly_proj_list)

Subroutine for timestepping with explicit runge kutta taylor

Arguments

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

The minimum refinement level of the mesh.
integer, intent(in) :: maxLevel

The maximum refinement level of the mesh.
integer, intent(in) :: currentLevel

The level the timestep has to be performed for.
type(atl_cube_container_type), intent(inout) :: cubes

Container for the cubical elements.
type(treelmesh_type), intent(in) :: tree

treelm mesh
type(atl_timestep_type), intent(inout) :: timestep_list(minLevel:)

List of levelwise timestepping algorihtms
integer, intent(in) :: nSteps

The number of steps of the time stepping scheme
type(atl_Equations_type), intent(inout) :: equation

The equation you are operating with.
type(tem_general_type), intent(inout) :: general

General treelm settings
integer, intent(inout) :: commStateTimer

Timer for measuring the communication time inside this routine.
type(ply_poly_project_type), intent(inout) :: poly_proj_list(:)

unique list for projection methods

private subroutine rktaylor_update(statedata_list, statedata_list_temp)

Subroutine calculates the final update step of the Runge-Kutta Taylor method. It is performing levelwise.

Arguments

Type IntentOptional Attributes Name
type(atl_statedata_type), intent(inout) :: statedata_list

List of states you want to calc the rhs for. For each level we have one.
type(atl_statedata_type), intent(inout) :: statedata_list_temp

List of levelwise timestepping algorihtms

private recursive subroutine rktaylor_substep(minLevel, maxLevel, currentLevel, mesh_list, tree, levelPointer, kerneldata_list, statedata_list, facedata_list, source, penalizationdata_list, boundary_list, bc, scheme_list, poly_proj_pos, poly_proj_list, timestep_list, equation, material_list, general, commStateTimer)

Subroutine calculates a substep of the Runge-Kutta-Taylor timestepping scheme. Calls itself recursively for the finer levels until the finest level is reached.

Arguments

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

The minimum refinement level of the mesh.
integer, intent(in) :: maxLevel

The maximum refinement level of the mesh.
integer, intent(in) :: currentLevel

The level the timestep has to be performed for.
type(atl_cube_elem_type), intent(inout) :: mesh_list(minLevel:maxLevel)

List of mesh parts. For each level we have one.
type(treelmesh_type), intent(in) :: tree

treelm mesh
integer, intent(in) :: levelPointer(:)

Pointer for elements from global treeID list index to index in levelwise fluid lists
type(atl_kerneldata_type), intent(inout) :: kerneldata_list(minLevel:maxLevel)

List of kerneldatas. For each level we have one
type(atl_statedata_type), intent(inout) :: statedata_list(minLevel:maxLevel)

List of states you want to calc the rhs for. For each level we have one.
type(atl_facedata_type), intent(inout) :: facedata_list(minLevel:maxLevel)

List of faces states you want to calc the rhs for. For each level we have one.
type(atl_source_type), intent(inout) :: source

List of sources, for each level
type(atl_penalizationData_type), intent(inout) :: penalizationdata_list(minLevel:maxLevel)

List of penalization data, for each level.
type(atl_level_boundary_type), intent(inout) :: boundary_list(minLevel:maxLevel)

List of boundaries, for each level.
type(atl_boundary_type), intent(in) :: bc(:)

Global description of the boundaries
type(atl_scheme_type), intent(inout) :: scheme_list(minLevel:maxLevel)

List of schemes, for each level.
integer, intent(in) :: poly_proj_pos(minLevel:maxLevel)

List of position of projection method in unique projection list, for each level
type(ply_poly_project_type), intent(inout) :: poly_proj_list(:)

unique list for projection methods
type(atl_timestep_type), intent(inout) :: timestep_list(minLevel:maxLevel)

List of levelwise timestepping algorihtms
type(atl_Equations_type), intent(inout) :: equation

The equation you are operating with.
type(atl_material_type), intent(inout) :: material_list(minlevel:maxlevel)

Material parameter description.
type(tem_general_type), intent(inout) :: general

General treelm settings
integer, intent(inout) :: commStateTimer

Timer for measuring the communication time inside this routine.