mod_face_advection_tvd_superbee Module Reference

Explicit dimensional splitting Lax-Wendroff TVD SuperBee (LW-TVD-SB) scheme for the advection equation. More...

Functions/Subroutines
subroutine	yee_roe_davis_tvd (dx_local, vel_field_local, divupsi_local, index_local, n, local_time_step)
	Fills \( \mathbf{u} \mathbf{\nabla} \mathbf{u} \) for the TVD scheme (Yee-Roe-Davis Symmetric Scheme)
subroutine	roe_sweby_tvd (dx_local, vel_field_local, divupsi_local, index_local, n, local_time_step)
	Fills \( \mathbf{u} \mathbf{\nabla} \mathbf{u} \) for the TVD scheme (Roe-Sweby Upwind TVD limiters)
subroutine	harten_tvd (dx_local, vel_field_local, divupsi_local, index_local, n, local_time_step)
	Fills \( \mathbf{u} \mathbf{\nabla} \mathbf{u} \) for the TVD scheme (Harten-Yee Upwind TVD limiters with new and old formation) w/ minmod.
subroutine	lw_tvd_linear (scalar_local, vel_field_2, divupsi_local, index_local, n, vel_variable_index, local_time_step)
	Fills \( \mathbf{u} \mathbf{\nabla} \mathbf{u} \) for the LW-TVD-SB scheme.
subroutine	face_tvd_superbee_splitting (vel_field, vel_field_2, divupsi, local_time_step, navier_splitting_time_coeff, navier_has_immersed_boundaries, navier_ib_has_one_sided_inner_discretization, navier_isd_target, navier_ib_inner_discretization_order, navier_boundary_condition, index_local_u, index_local_v, index_local_w, n)
subroutine	face_advection_tvd_superbee (velocity, density_face, divupsi, navier_boundary_condition, navier_nonlinear_term_splitting_scheme, navier_has_immersed_boundaries, navier_ib_has_one_sided_inner_discretization, navier_isd_target, navier_ib_inner_discretization_order, navier_splitting_time_coeff, time_step)
	Calculates \( \partial \mathbf{u}/\partial t = - \mathbf{u} \mathbf{\nabla} \mathbf{u} \) with the LW-TVD-SB scheme.

Variables
logical, parameter	force_first_order = .false.

Detailed Description

Be aware that this is not a conservative scheme but a traditional advection scheme.

The equation solved is:

\[ \frac{\partial \mathbf{u}}{\partial t} + \mathbf{u} \mathbf{\nabla} \mathbf{u} = 0 \]

Function/Subroutine Documentation

face_advection_tvd_superbee()

subroutine mod_face_advection_tvd_superbee::face_advection_tvd_superbee	(	type(t_face_field), intent(in)	velocity,
		type(t_face_field), intent(in)	density_face,
		type(t_face_field), intent(inout)	divupsi,
		type(t_boundary_condition_face), intent(in)	navier_boundary_condition,
		integer, intent(in)	navier_nonlinear_term_splitting_scheme,
		logical, intent(in)	navier_has_immersed_boundaries,
		logical, intent(in)	navier_ib_has_one_sided_inner_discretization,
		integer, dimension(:), intent(in)	navier_isd_target,
		integer, dimension(:), intent(in)	navier_ib_inner_discretization_order,
		double precision, dimension(3), intent(in)	navier_splitting_time_coeff,
		double precision, intent(in)	time_step )

Parameters

[in]	velocity	the velocity \( \mathbf{u} \)
[in]	density_face	face centered density field
[in,out]	divupsi	\( \mathbf{u^{n^*}} \)
[in]	navier_boundary_condition	Boundary conditions
[in]	navier_nonlinear_term_splitting_scheme
[in]	navier_has_immersed_boundaries
[in]	navier_ib_has_one_sided_inner_discretization
[in]	navier_isd_target
[in]	navier_ib_inner_discretization_order
[in]	navier_splitting_time_coeff
[in]	time_step	the time step \( \delta t = t^{n+1} - t^n \)

harten_tvd()

subroutine mod_face_advection_tvd_superbee::harten_tvd	(	double precision, dimension (:), intent(in)	dx_local,
		double precision, dimension (:,:,:), intent(in)	vel_field_local,
		double precision, dimension (:,:,:), intent(inout)	divupsi_local,
		integer, dimension (:,:), intent(in)	index_local,
		integer, intent(in)	n,
		double precision, intent(in)	local_time_step )

Parameters

[in]	dx_local	grid step
[in]	vel_field_local	intermediate velocity
[in,out]	divupsi_local	\( \mathbf{u} \mathbf{\nabla} \mathbf{u} \)
[in]	index_local	upper and lower index limits for given spatial direction
[in]	n	spatial direction
[in]	local_time_step	local time step

lw_tvd_linear()

subroutine mod_face_advection_tvd_superbee::lw_tvd_linear	(	double precision, dimension (:,:,:), intent(in)	scalar_local,
		type(t_face_field), intent(in)	vel_field_2,
		double precision, dimension (:,:,:), intent(inout)	divupsi_local,
		integer, dimension (:,:), intent(in)	index_local,
		integer, intent(in)	n,
		integer, intent(in)	vel_variable_index,
		double precision, intent(in)	local_time_step )

Parameters

[in]	scalar_local	numerical flux
[in]	vel_field_2	velocity field pre operator splitting
[in,out]	divupsi_local	\( \mathbf{u} \mathbf{\nabla} \mathbf{u} \)
[in]	index_local	upper and lower index limits for given spatial direction
[in]	n	spatial direction
[in]	vel_variable_index	which velocity variable is being used (1) u (2) v (3) w
[in]	local_time_step	local time step

roe_sweby_tvd()

subroutine mod_face_advection_tvd_superbee::roe_sweby_tvd	(	double precision, dimension (:), intent(in)	dx_local,
		double precision, dimension (:,:,:), intent(in)	vel_field_local,
		double precision, dimension (:,:,:), intent(inout)	divupsi_local,
		integer, dimension (:,:), intent(in)	index_local,
		integer, intent(in)	n,
		double precision, intent(in)	local_time_step )

Parameters

[in]	dx_local	grid step
[in]	vel_field_local	intermediate velocity
[in,out]	divupsi_local	\( \mathbf{u} \mathbf{\nabla} \mathbf{u} \)
[in]	index_local	upper and lower index limits for given spatial direction
[in]	n	spatial direction
[in]	local_time_step	local time step

yee_roe_davis_tvd()

subroutine mod_face_advection_tvd_superbee::yee_roe_davis_tvd	(	double precision, dimension (:), intent(in)	dx_local,
		double precision, dimension (:,:,:), intent(in)	vel_field_local,
		double precision, dimension (:,:,:), intent(inout)	divupsi_local,
		integer, dimension (:,:), intent(in)	index_local,
		integer, intent(in)	n,
		double precision, intent(in)	local_time_step )

Parameters

[in]	dx_local	grid step
[in]	vel_field_local	intermediate velocity
[in,out]	divupsi_local	\( \mathbf{u} \mathbf{\nabla} \mathbf{u} \)
[in]	index_local	upper and lower index limits for given spatial direction
[in]	n	spatial direction
[in]	local_time_step	local time step