Partial Differential Equations on faces

First level routines to discretize PDE term by term on faces. More...

Topics
	Stress tensor divergence term
	Add to matrix the viscous stress term of Navier equation.

Namespaces
module	mod_momentum_boundary_conditions
	Boundary conditions related routines for momentum.
module	enum_navier_nonlinear_term_scheme
	Discretization schemes for the nonlinear momentum term.
module	mod_face_vector_implicit_discretization_collection
	Module that encapsulates all face vector term by term discretization modules.

Functions
subroutine	mod_discretize_face_temporal_term::discretize_face_temporal_term (matrix, rhs, density_face_n, density_face_star, velocity_n, velocity_nm1, equation_time_step, equation_time_step_n, equation_time_order_discretization, is_momentum_preserving_method, equation_stencil, equation_ls_map)
	Discretize the advection term.
subroutine	mod_discretize_nonlinear_momentum_term::discretize_nonlinear_momentum_term (matrix, navier_nonlinear_term_discretization_type, navier_nonlinear_term_scheme, navier_has_div_u_advection_term, is_navier_momentum_preserving_method, navier_has_immersed_boundaries, navier_ib_has_one_sided_inner_discretization, navier_isd_target, navier_ib_inner_discretization_order, density_face_n, density_face_star, divergence_extrapolated, time_step_nm1, time_step, cfl_navier_advection, velocity_extrapolated, velocity_nm1, velocity_n, explicit_time_order_discretization, explicit_specify_temporal_stability_factor, explicit_temporal_stability_factor, flux_type, explicit_nonlinear_term_n, navier_stencil, navier_ls_map, boundary_condition)
	Add nonlinear momentum term to the given linear system.

Detailed Description

In this directory you will find the first level of routines to solve PDE term by term on face based variables.

Function Documentation

discretize_face_temporal_term()

subroutine mod_discretize_face_temporal_term::discretize_face_temporal_term	(	double precision, dimension(:), intent(inout)	matrix,
		double precision, dimension(:), intent(inout)	rhs,
		type(t_face_field), intent(in)	density_face_n,
		type(t_face_field), intent(in)	density_face_star,
		type(t_face_field), intent(in)	velocity_n,
		type(t_face_field), intent(in)	velocity_nm1,
		double precision, intent(in)	equation_time_step,
		double precision, intent(in)	equation_time_step_n,
		integer, intent(in)	equation_time_order_discretization,
		logical, intent(in)	is_momentum_preserving_method,
		type(t_face_stencil), intent(in)	equation_stencil,
		type(t_face_ls_map), intent(in)	equation_ls_map )

This term is treated implicitly thanks to backward first order Euler scheme or a second order Backward Differentiation Formula.

The diagonal of the matrix and the right-hand-side are modified accordingly to the scheme chosen.

Parameters

[in,out]	matrix,rhs	linear system
[in]	density_face_n
[in]	density_face_star
[in]	velocity_n
[in]	velocity_nm1
[in]	equation_time_step
[in]	equation_time_step_n
[in]	equation_time_order_discretization
[in]	is_momentum_preserving_method
[in]	equation_stencil
[in]	equation_ls_map

discretize_nonlinear_momentum_term()

subroutine mod_discretize_nonlinear_momentum_term::discretize_nonlinear_momentum_term	(	double precision, dimension(:), intent(inout)	matrix,
		integer, intent(in)	navier_nonlinear_term_discretization_type,
		integer, intent(in)	navier_nonlinear_term_scheme,
		logical, intent(in)	navier_has_div_u_advection_term,
		logical, intent(in)	is_navier_momentum_preserving_method,
		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,
		type(t_face_field), intent(in)	density_face_n,
		type(t_face_field), intent(in)	density_face_star,
		double precision, dimension(:,:,:), intent(in)	divergence_extrapolated,
		double precision, intent(in)	time_step_nm1,
		double precision, intent(in)	time_step,
		double precision, intent(inout)	cfl_navier_advection,
		type(t_face_field), intent(inout)	velocity_extrapolated,
		type(t_face_field), intent(inout)	velocity_nm1,
		type(t_face_field), intent(inout)	velocity_n,
		integer, intent(in)	explicit_time_order_discretization,
		logical, intent(in)	explicit_specify_temporal_stability_factor,
		double precision, intent(in)	explicit_temporal_stability_factor,
		type(t_fv_flux), intent(in)	flux_type,
		type(t_face_field), intent(inout)	explicit_nonlinear_term_n,
		type(t_face_stencil), intent(in)	navier_stencil,
		type(t_face_ls_map), intent(in)	navier_ls_map,
		type(t_boundary_condition_face), intent(in)	boundary_condition )

The nonlinear momentum term is written as follows:

\[ \rho \mathbf{u} \mathbf{\nabla} \mathbf{u} = \rho \nabla \cdot (\mathbf{u} \otimes \mathbf{u}) - \rho \mathbf{u} \nabla \cdot(\mathbf{u}), \]

where each term is discretized separately. The term \(\nabla \cdot (\mathbf{u} \otimes \mathbf{u})\) is a vector that can be decomposed as:

\[ \nabla \cdot (\mathbf{u} \otimes \mathbf{u}) = \left[ \begin{matrix} \nabla \cdot (u \times \mathbf{u}) \\ \nabla \cdot (v \times \mathbf{u}) \\ \nabla \cdot (w \times \mathbf{u}) \end{matrix} \right] \]