Cell linear system preparation

Cell linear system preparation of a scalar equation defined on cells. More...

Namespaces
module	type_ls_map
	Type declaration associated to the numerical grid mapping of a cell linear system.

Functions
subroutine	mod_add_diagonal_cell_matrix::add_diagonal_cell_matrix (matrix, stencil_size, work_array, equation_ls_map)
	Add a term to the diagonal of a matrix for a cell-discretized equation.
subroutine	mod_add_rhs_cell::add_rhs_cell (rhs, array, equation_ls_map)
	Add a term to the right-hand side for a cell-discretized equation or determine \( \phi^{n+1} \) for a fully explicit cell transport implementation.
subroutine	mod_finalize_cell_linear_system::finalize_cell_linear_system (matrix, rhs, stencil_size, equation_ls_map)
	Finalize a cell linear system. The routine checks the if a diagonal element of the matrix is null (typically a corner of the domain), set it to 1 and the right-hand side to 0.
subroutine	mod_initialize_cell_linear_system::initialize_cell_linear_system (matrix, rhs, ls_map)
	Allocate matrix and right-hand-side of a cell linear system.
subroutine	mod_time_advance_explicitly::time_advance_explicitly (matrix, rhs, array, equation_ls_map, stencil_size, boundary_condition)
	Determine \( \phi^{n+1} \) for a fully explicit cell transport implementation.

Detailed Description

Function Documentation

add_diagonal_cell_matrix()

subroutine mod_add_diagonal_cell_matrix::add_diagonal_cell_matrix	(	double precision, dimension(:), intent(inout)	matrix,
		integer, intent(in)	stencil_size,
		double precision, dimension(nx,ny,nz), intent(in)	work_array,
		type(t_ls_map), intent(in)	equation_ls_map )

This routine takes cell field elements and adds them to the corresponding diagonal.

add_rhs_cell()

subroutine mod_add_rhs_cell::add_rhs_cell	(	double precision, dimension(:), intent(inout)	rhs,
		double precision, dimension(nx,ny,nz), intent(in)	array,
		type(t_ls_map), intent(in)	equation_ls_map )

Note

• The add_rhs_cell routine takes cell field elements and adds them to the right-hand side of a linear system.
• The time_advance_explicitly routine solves \(\alpha_{i,j,k} \phi^{n+1} = RHS_{i,j,k} \) and applies the appropriate boundary conditions.

finalize_cell_linear_system()

subroutine mod_finalize_cell_linear_system::finalize_cell_linear_system	(	double precision, dimension(:), intent(inout)	matrix,
		double precision, dimension(:), intent(inout)	rhs,
		integer, intent(in)	stencil_size,
		type(t_ls_map), intent(in)	equation_ls_map )

Todo

improve unused nodes values

time_advance_explicitly()

subroutine mod_time_advance_explicitly::time_advance_explicitly	(	double precision, dimension(:), intent(in)	matrix,
		double precision, dimension(:), intent(in)	rhs,
		double precision, dimension(nx,ny,nz), intent(out)	array,
		type(t_ls_map), intent(in)	equation_ls_map,
		integer, intent(in)	stencil_size,
		type(t_boundary_condition), intent(in)	boundary_condition )

Note

• The time_advance_explicitly routine solves \(\alpha_{i,j,k} \phi^{n+1} = RHS_{i,j,k} \) and applies the appropriate boundary conditions.