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, cfl_coefficient, 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. More...
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, cfl_coefficient, 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. More...
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, cfl_coefficient, 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. More...
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, cfl_coefficient, 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. More...
subroutine	integrate_cell_advection_term_explicit_generic_nssp32 (divut, time_step, dt_nm1, dt_n, velocity_nm1, velocity_n, velocity_np1, scalar, divut_term_computer, flux_type, cfl_coefficient, boundary_condition)
	Adds the advection term \( c \nabla \cdot ( \mathbf{u} \phi ) \) with a generic spatial scheme. More...
subroutine	integrate_cell_advection_term_explicit_generic_nssp32_split (divut, time_step, dt_nm1, dt_n, velocity_nm1, velocity_n, velocity_np1, scalar, divut_term_computer, flux_type, cfl_coefficient, boundary_condition)
	Integrate the advection term \( c \nabla \cdot ( \mathbf{u} \phi ) \) with a generic spatial scheme. The temporal scheme is a 3 steps NSSP at 2nd order (NSSP32). The integration is done in a split manner (x then y then z)
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, cfl_coefficient, boundary_condition)
	Adds the advection term \( c \nabla \cdot ( \mathbf{u} \phi ) \) with a generic spatial scheme. More...
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, cfl_coefficient, 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

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)	cfl_coefficient,
		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
	)

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]	divut_term_computer_fd	the procedure that will compute the div(u phi) term giving u and phi for FD WENO schemes
[in]	cfl_coefficient	the cfl coefficient to use (depending on the time and space schemes)
[in]	equation_isd_target	Subset of immersed boundaries.
[in]	ibc_variable	boundary conditions on immersed boundaries.
[in]	boundary_condition

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)	cfl_coefficient,
		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
	)

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]	divut_term_computer_fd	the procedure that will compute the div(u phi) term giving u and phi for FD WENO schemes
[in]	cfl_coefficient	the cfl coefficient to use (depending on the time and space schemes)

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)	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)	cfl_coefficient,
		type(t_boundary_condition), intent(in)	boundary_condition
	)

Optimized version for 3 stages at order 2

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]	cfl_coefficient	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)	cfl_coefficient,
		type(t_boundary_condition), intent(in)	boundary_condition
	)

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]	divut_term_computer_fd	the procedure that will compute the div(u phi) term giving u and phi for FD WENO schemes
[in]	flux_type	the flux type to use for the explicit advection (type_fv_flux)
[in]	cfl_coefficient	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)	cfl_coefficient,
		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
	)

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]	divut_term_computer_fd	the procedure that will compute the div(u phi) term giving u and phi for FD WENO schemes
[in]	flux_type	the flux type to use for the explicit advection (type_fv_flux)
[in]	cfl_coefficient	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)	cfl_coefficient,
		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
	)

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]	cfl_coefficient	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