mod_integrate_cell_advection_term_explicit_generic Module Reference

Integration methods for the advection equation. More...

Data Types
interface	divut_term_computer_interface
	The abstract function for computing div(U phi) More...
interface	divut_term_computer_interface_fd
	The abstract function for computing div(U phi) for the FD WENO schemes. More...

Functions/Subroutines
subroutine	integrate_cell_advection_term_explicit_generic_euler (divut, time_step, dt_nm1, dt_n, velocity_nm1, velocity_n, velocity_np1, scalar, divut_term_computer, flux_type, temporal_stability_factor, equation_has_immersed_boundaries, equation_isd_target, ibc_variable, boundary_condition)
	Adds the advection term \( c \nabla \cdot ( \mathbf{u} \phi ) \) with a generic spatial scheme euler (in time) version.
subroutine	integrate_cell_advection_term_explicit_generic_euler_split (divut, time_step, dt_nm1, dt_n, velocity_nm1, velocity_n, velocity_np1, scalar, divut_term_computer, flux_type, temporal_stability_factor, equation_has_immersed_boundaries, equation_isd_target, ibc_variable, boundary_condition)
	Adds the advection term \( c \nabla \cdot ( \mathbf{u} \phi ) \) with a generic spatial scheme euler (in time) version.
subroutine	integrate_cell_advection_term_explicit_generic_sspso (divut, time_step, dt_nm1, dt_n, velocity_nm1, velocity_n, velocity_np1, scalar, divut_term_computer, flux_type, temporal_stability_factor, aki, bi, ci, boundary_condition)
	Adds the advection term \( c \nabla \cdot ( \mathbf{u} \phi ) \) with a generic spatial scheme SSP 2 stage 2nd order without velocity extrapolation.
subroutine	integrate_cell_advection_term_explicit_generic_sspso_split (divut, time_step, dt_nm1, dt_n, velocity_nm1, velocity_n, velocity_np1, scalar, divut_term_computer, flux_type, temporal_stability_factor, aki, bi, ci, boundary_condition)
	Adds the advection term \( c \nabla \cdot ( \mathbf{u} \phi ) \) with a generic spatial scheme in a splitted manner SSP 2 stage 2nd order without velocity extrapolation.
subroutine	integrate_cell_advection_term_explicit_generic_nssp32 (scalar_star, time_step_n, time_step, velocity_nm1, velocity_n, scalar_n, divut_term_computer, flux_type, temporal_stability_factor, boundary_condition)
	Adds the advection term \( c \nabla \cdot ( \mathbf{u} \phi ) \) with a generic spatial scheme.
subroutine	integrate_cell_advection_term_explicit_generic_nssp32_split (scalar_star, time_step_n, time_step, velocity_nm1, velocity_n, scalar_n, divut_term_computer, flux_type, temporal_stability_factor, boundary_condition)
	Adds the advection term \( c \nabla \cdot ( \mathbf{u} \phi ) \) with a generic spatial scheme.
subroutine	integrate_cell_advection_term_explicit_generic_nssp53 (divut, time_step, dt_nm1, dt_n, velocity_nm1, velocity_n, velocity_np1, scalar, divut_term_computer, flux_type, temporal_stability_factor, boundary_condition)
	Adds the advection term \( c \nabla \cdot ( \mathbf{u} \phi ) \) with a generic spatial scheme.
subroutine	integrate_cell_advection_term_explicit_generic_nssp53_split (divut, time_step, dt_nm1, dt_n, velocity_nm1, velocity_n, velocity_np1, scalar, divut_term_computer, flux_type, temporal_stability_factor, boundary_condition)
	Integrate the advection term \( c \nabla \cdot ( \mathbf{u} \phi ) \) with a generic spatial scheme. The temporal scheme is a 5 steps NSSP at 3nd order (NSSP53). The integration is done in a split manner (x then y then z)

Detailed Description

Integration methods for the advection equation.

This module furnishes various temporal integration schemes (mainly RK schemes) for the advection equation. As the explicit resolution of the advection equation is subjected to a stability condition (the CFL), sub iterations can occur during the integration process.

Note

A generic abstract function divut_term_computer_interface is defined for simplifying the process. With this manner, any spatial scheme can be used, may it be first order or WENO.

Function/Subroutine Documentation

integrate_cell_advection_term_explicit_generic_euler()

subroutine mod_integrate_cell_advection_term_explicit_generic::integrate_cell_advection_term_explicit_generic_euler	(	double precision, dimension(:,:,:), intent(inout)	divut,
		double precision, intent(in)	time_step,
		double precision, intent(in)	dt_nm1,
		double precision, intent(in)	dt_n,
		type(t_face_field), intent(in)	velocity_nm1,
		type(t_face_field), intent(in)	velocity_n,
		type(t_face_field), intent(in)	velocity_np1,
		double precision, dimension(:,:,:), intent(in)	scalar,
		procedure(divut_term_computer_interface)	divut_term_computer,
		type(t_fv_flux), intent(in)	flux_type,
		double precision, intent(in)	temporal_stability_factor,
		logical, intent(in)	equation_has_immersed_boundaries,
		integer, dimension(:), intent(in)	equation_isd_target,
		type(t_immersed_boundary_condition), dimension(:), intent(in)	ibc_variable,
		type(t_boundary_condition), intent(in)	boundary_condition )

Adds the advection term \( c \nabla \cdot ( \mathbf{u} \phi ) \) with a generic spatial scheme euler (in time) version.

Parameters

[in,out]	divut	the resulting term
[in]	time_step	the time step on which we integrate (might be different from dt_n for sub integration steps!)
[in]	velocity_nm1	velocity field at \( t^{n-1} \)
[in]	velocity_n	velocity field at \( t^n \)
[in]	velocity_np1	velocity field at \( t^{n+1} \)
[in]	dt_nm1	the previous time step \( \delta t^{n-1} = t^{n} - t^{n-1} \)
[in]	dt_n	the current time step \( \delta t^{n} = t^{n+1} - t^{n} \)
[in]	flux_type	the flux type to use for the explicit advection (type_fv_flux)
[in]	boundary_condition	the boundary conditions of the cell scalar
[in]	scalar	the scalar to advect
[in]	divut_term_computer	the procedure that will compute the div(u phi) term giving u and phi
[in]	temporal_stability_factor	the cfl coefficient to use (depending on the time and space schemes)
[in]	equation_has_immersed_boundaries	true if has IBC
[in]	equation_isd_target	Subset of immersed boundaries.
[in]	ibc_variable	boundary conditions on immersed boundaries.

integrate_cell_advection_term_explicit_generic_euler_split()

subroutine mod_integrate_cell_advection_term_explicit_generic::integrate_cell_advection_term_explicit_generic_euler_split	(	double precision, dimension(:,:,:), intent(inout)	divut,
		double precision, intent(in)	time_step,
		double precision, intent(in)	dt_nm1,
		double precision, intent(in)	dt_n,
		type(t_face_field), intent(in)	velocity_nm1,
		type(t_face_field), intent(in)	velocity_n,
		type(t_face_field), intent(in)	velocity_np1,
		double precision, dimension(:,:,:), intent(in)	scalar,
		procedure(divut_term_computer_interface)	divut_term_computer,
		type(t_fv_flux), intent(in)	flux_type,
		double precision, intent(in)	temporal_stability_factor,
		logical, intent(in)	equation_has_immersed_boundaries,
		integer, dimension(:), intent(in)	equation_isd_target,
		type(t_immersed_boundary_condition), dimension(:), intent(in)	ibc_variable,
		type(t_boundary_condition), intent(in)	boundary_condition )

Adds the advection term \( c \nabla \cdot ( \mathbf{u} \phi ) \) with a generic spatial scheme euler (in time) version.

Parameters

[in,out]	divut	the resulting term
[in]	time_step	the time step on which we integrate (might be different from dt_n for sub integration steps!)
[in]	velocity_nm1	velocity field at \( t^{n-1} \)
[in]	velocity_n	velocity field at \( t^n \)
[in]	velocity_np1	velocity field at \( t^{n+1} \)
[in]	dt_nm1	the previous time step \( \delta t^{n-1} = t^{n} - t^{n-1} \)
[in]	dt_n	the current time step \( \delta t^{n} = t^{n+1} - t^{n} \)
[in]	flux_type	the flux type to use for the explicit advection (type_fv_flux)
[in]	boundary_condition	the boundary conditions of the cell scalar
[in]	scalar	the scalar to advect
[in]	divut_term_computer	the procedure that will compute the div(u phi) term giving u and phi
[in]	temporal_stability_factor	the cfl coefficient to use (depending on the time and space schemes)
[in]	equation_has_immersed_boundaries	true if has IBC
[in]	equation_isd_target	Subset of immersed boundaries.
[in]	ibc_variable	boundary conditions on immersed boundaries.

integrate_cell_advection_term_explicit_generic_nssp32()

subroutine mod_integrate_cell_advection_term_explicit_generic::integrate_cell_advection_term_explicit_generic_nssp32	(	double precision, dimension(:,:,:), intent(inout)	scalar_star,
		double precision, intent(in)	time_step_n,
		double precision, intent(in)	time_step,
		type(t_face_field), intent(in)	velocity_nm1,
		type(t_face_field), intent(in)	velocity_n,
		double precision, dimension(:,:,:), intent(in)	scalar_n,
		procedure(divut_term_computer_interface)	divut_term_computer,
		type(t_fv_flux), intent(in)	flux_type,
		double precision, intent(in)	temporal_stability_factor,
		type(t_boundary_condition), intent(in)	boundary_condition )

Adds the advection term \( c \nabla \cdot ( \mathbf{u} \phi ) \) with a generic spatial scheme.

Optimized version for 3 stages at order 2

Parameters

[in,out]	scalar_star	the resulting field
[in]	time_step_n	the previous time step \( \delta t^{n-1} = t^{n} - t^{n-1} \)
[in]	time_step	the time step on which we integrate (might be different from dt_n for sub integration steps!)
[in]	velocity_nm1	velocity field at \( t^{n-1} \)
[in]	velocity_n	velocity field at \( t^n \)
[in]	scalar_n	the scalar to advect at time \( t^{n} \)
[in]	divut_term_computer	the procedure that will compute the div(u phi) term giving u and phi
[in]	flux_type	the flux type to use for the explicit advection (type_fv_flux)
[in]	temporal_stability_factor	the cfl coefficient to use (depending on the time and space schemes)
[in]	boundary_condition	the boundary conditions of the cell scalar

integrate_cell_advection_term_explicit_generic_nssp32_split()

subroutine mod_integrate_cell_advection_term_explicit_generic::integrate_cell_advection_term_explicit_generic_nssp32_split	(	double precision, dimension(:,:,:), intent(inout)	scalar_star,
		double precision, intent(in)	time_step_n,
		double precision, intent(in)	time_step,
		type(t_face_field), intent(in)	velocity_nm1,
		type(t_face_field), intent(in)	velocity_n,
		double precision, dimension(:,:,:), intent(in)	scalar_n,
		procedure(divut_term_computer_interface)	divut_term_computer,
		type(t_fv_flux), intent(in)	flux_type,
		double precision, intent(in)	temporal_stability_factor,
		type(t_boundary_condition), intent(in)	boundary_condition )

Adds the advection term \( c \nabla \cdot ( \mathbf{u} \phi ) \) with a generic spatial scheme.

Optimized version for 3 stages at order 2 The integration is done in a split manner (x then y then z)

Parameters

[in,out]	scalar_star	the resulting field
[in]	time_step_n	the previous time step \( \delta t^{n-1} = t^{n} - t^{n-1} \)
[in]	time_step	the time step on which we integrate (might be different from dt_n for sub integration steps!)
[in]	velocity_nm1	velocity field at \( t^{n-1} \)
[in]	velocity_n	velocity field at \( t^n \)
[in]	scalar_n	the scalar to advect at time \( t^{n} \)
[in]	divut_term_computer	the procedure that will compute the div(u phi) term giving u and phi
[in]	flux_type	the flux type to use for the explicit advection (type_fv_flux)
[in]	temporal_stability_factor	the cfl coefficient to use (depending on the time and space schemes)
[in]	boundary_condition	the boundary conditions of the cell scalar

integrate_cell_advection_term_explicit_generic_nssp53()

subroutine mod_integrate_cell_advection_term_explicit_generic::integrate_cell_advection_term_explicit_generic_nssp53	(	double precision, dimension(:,:,:), intent(inout)	divut,
		double precision, intent(in)	time_step,
		double precision, intent(in)	dt_nm1,
		double precision, intent(in)	dt_n,
		type(t_face_field), intent(in)	velocity_nm1,
		type(t_face_field), intent(in)	velocity_n,
		type(t_face_field), intent(in)	velocity_np1,
		double precision, dimension(:,:,:), intent(in)	scalar,
		procedure(divut_term_computer_interface)	divut_term_computer,
		type(t_fv_flux), intent(in)	flux_type,
		double precision, intent(in)	temporal_stability_factor,
		type(t_boundary_condition), intent(in)	boundary_condition )

Adds the advection term \( c \nabla \cdot ( \mathbf{u} \phi ) \) with a generic spatial scheme.

Optimized version for 5 stages at order 3

Parameters

[in,out]	divut	the resulting field
[in]	time_step	the time step on which we integrate (might be different from dt_n for sub integration steps!)
[in]	velocity_nm1	velocity field at \( t^{n-1} \)
[in]	velocity_n	velocity field at \( t^n \)
[in]	velocity_np1	velocity field at \( t^{n+1} \)
[in]	dt_nm1	the previous time step \( \delta t^{n-1} = t^{n} - t^{n-1} \)
[in]	dt_n	the current time step \( \delta t^{n} = t^{n+1} - t^{n} \)
[in]	scalar	the scalar to advect
[in]	divut_term_computer	the procedure that will compute the div(u phi) term giving u and phi
[in]	flux_type	the flux type to use for the explicit advection (type_fv_flux)
[in]	temporal_stability_factor	the cfl coefficient to use (depending on the time and space schemes)
[in]	boundary_condition	the boundary conditions of the cell scalar

integrate_cell_advection_term_explicit_generic_sspso()

subroutine mod_integrate_cell_advection_term_explicit_generic::integrate_cell_advection_term_explicit_generic_sspso	(	double precision, dimension(:,:,:), intent(inout)	divut,
		double precision, intent(in)	time_step,
		double precision, intent(in)	dt_nm1,
		double precision, intent(in)	dt_n,
		type(t_face_field), intent(in)	velocity_nm1,
		type(t_face_field), intent(in)	velocity_n,
		type(t_face_field), intent(in)	velocity_np1,
		double precision, dimension(:,:,:), intent(in)	scalar,
		procedure(divut_term_computer_interface)	divut_term_computer,
		type(t_fv_flux), intent(in)	flux_type,
		double precision, intent(in)	temporal_stability_factor,
		double precision, dimension(:,:), intent(in)	aki,
		double precision, dimension(:), intent(in)	bi,
		double precision, dimension(:), intent(in)	ci,
		type(t_boundary_condition), intent(in)	boundary_condition )

Adds the advection term \( c \nabla \cdot ( \mathbf{u} \phi ) \) with a generic spatial scheme SSP 2 stage 2nd order without velocity extrapolation.

Parameters

[in,out]	divut	the resulting field
[in]	time_step	the time step on which we integrate (might be different from dt_n for sub integration steps!)
[in]	velocity_nm1	velocity field at \( t^{n-1} \)
[in]	velocity_n	velocity field at \( t^n \)
[in]	velocity_np1	velocity field at \( t^{n+1} \)
[in]	dt_nm1	the previous time step \( \delta t^{n-1} = t^{n} - t^{n-1} \)
[in]	dt_n	the current time step \( \delta t^{n} = t^{n+1} - t^{n} \)
[in]	scalar	the scalar to advect
[in]	divut_term_computer	the procedure that will compute the div(u phi) term giving u and phi
[in]	flux_type	the flux type to use for the explicit advection (type_fv_flux)
[in]	temporal_stability_factor	the cfl coefficient to use (depending on the time and space schemes)
[in]	boundary_condition	the boundary conditions of the cell scalar
[in]	aki,bi,ci	the given coefficients of the Butcher tableau

integrate_cell_advection_term_explicit_generic_sspso_split()

subroutine mod_integrate_cell_advection_term_explicit_generic::integrate_cell_advection_term_explicit_generic_sspso_split	(	double precision, dimension(:,:,:), intent(inout)	divut,
		double precision, intent(in)	time_step,
		double precision, intent(in)	dt_nm1,
		double precision, intent(in)	dt_n,
		type(t_face_field), intent(in)	velocity_nm1,
		type(t_face_field), intent(in)	velocity_n,
		type(t_face_field), intent(in)	velocity_np1,
		double precision, dimension(:,:,:), intent(in)	scalar,
		procedure(divut_term_computer_interface)	divut_term_computer,
		type(t_fv_flux), intent(in)	flux_type,
		double precision, intent(in)	temporal_stability_factor,
		double precision, dimension(:,:), intent(in)	aki,
		double precision, dimension(:), intent(in)	bi,
		double precision, dimension(:), intent(in)	ci,
		type(t_boundary_condition), intent(in)	boundary_condition )

Adds the advection term \( c \nabla \cdot ( \mathbf{u} \phi ) \) with a generic spatial scheme in a splitted manner SSP 2 stage 2nd order without velocity extrapolation.

Parameters

[in,out]	divut	the resulting field
[in]	time_step	the time step on which we integrate (might be different from dt_n for sub integration steps!)
[in]	velocity_nm1	velocity field at \( t^{n-1} \)
[in]	velocity_n	velocity field at \( t^n \)
[in]	velocity_np1	velocity field at \( t^{n+1} \)
[in]	dt_nm1	the previous time step \( \delta t^{n-1} = t^{n} - t^{n-1} \)
[in]	dt_n	the current time step \( \delta t^{n} = t^{n+1} - t^{n} \)
[in]	scalar	the scalar to advect
[in]	divut_term_computer	the procedure that will compute the div(u phi) term giving u and phi
[in]	flux_type	the flux type to use for the explicit advection (type_fv_flux)
[in]	temporal_stability_factor	the cfl coefficient to use (depending on the time and space schemes)
[in]	boundary_condition	the boundary conditions of the cell scalar
[in]	aki,bi,ci	the given coefficients of the Butcher tableau