cs_cdo_diffusion.cpp File Reference

Build discrete stiffness matrices and handled boundary conditions for diffusion term in CDO vertex-based and vertex+cell schemes. More...

#include "cs_defs.h"
#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <math.h>
#include <bft_mem.h>
#include "cs_hodge.h"
#include "cs_log.h"
#include "cs_math.h"
#include "cs_property.h"
#include "cs_reco.h"
#include "cs_reco_cw.h"
#include "cs_scheme_geometry.h"
#include "cs_cdo_diffusion.h"

Include dependency graph for cs_cdo_diffusion.cpp:

Functions
void	cs_cdo_diffusion_pena_dirichlet (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account Dirichlet BCs by a weak enforcement by a penalization technique with a huge value. Predefined prototype to match the function pointer cs_cdo_enforce_bc_t. More...
void	cs_cdo_diffusion_pena_block_dirichlet (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account Dirichlet BCs by a weak enforcement by a penalization technique with a huge value. Case of a cellwise system defined by block. Predefined prototype to match the function pointer cs_cdo_enforce_bc_t. More...
void	cs_cdo_diffusion_alge_dirichlet (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account Dirichlet BCs by keeping the DoFs related to Dirichlet BCs in the algebraic system (i.e. a weak enforcement). The corresponding DoFs are algebraically "removed" of the system. More...
void	cs_cdo_diffusion_alge_dirichlet_extra_block (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Function close to cs_cdo_diffusion_alge_dirichlet but dedicated to systems by blocks and especially for extra-diagonal blocks. The treatment of the RHS is a bit different. More...
void	cs_cdo_diffusion_alge_block_dirichlet (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account Dirichlet BCs by keeping the DoFs related to Dirichlet BCs in the algebraic system (i.e. a weak enforcement) The corresponding DoFs are algebraically "removed" of the system Block version. More...
void	cs_cdo_diffusion_sfb_weak_dirichlet (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account Dirichlet BCs by a weak enforcement using Nitsche technique. Case of scalar-valued CDO Face-based schemes Predefined prototype to match the function pointer cs_cdo_enforce_bc_t. More...
void	cs_cdo_diffusion_vfb_weak_dirichlet (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account Dirichlet BCs by a weak enforcement using Nitsche technique. Case of vector-valued CDO Face-based schemes The idea is to compute the scalar version and dispatch it three times, one for each Cartesian components Predefined prototype to match the function pointer cs_cdo_enforce_bc_t. More...
void	cs_cdo_diffusion_sfb_wsym_dirichlet (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account Dirichlet BCs by a weak enforcement using Nitsche technique plus a symmetric treatment Case of scalar-valued CDO Face-based schemes Predefined prototype to match the function pointer cs_cdo_enforce_bc_t. More...
void	cs_cdo_diffusion_vfb_wsym_dirichlet (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account Dirichlet BCs by a weak enforcement using Nitsche technique plus a symmetric treatment. Case of vector-valued CDO Face-based schemes The idea is to compute the scalar version and dispatch it three times, one for each Cartesian components Predefined prototype to match the function pointer cs_cdo_enforce_bc_t. More...
void	cs_cdo_diffusion_vfb_wsym_sliding (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account sliding BCs by a weak enforcement using Nitsche technique plus a symmetric treatment. Case of vector-valued CDO Face-based schemes Predefined prototype to match the function pointer cs_cdo_enforce_bc_t. More...
void	cs_cdo_diffusion_sfb_cost_robin (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account Robin BCs. Case of scalar-valued CDO-Fb schemes with a CO+ST algorithm. Predefined prototype to match the function pointer cs_cdo_enforce_bc_t. More...
void	cs_cdo_diffusion_svb_cost_robin (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account Robin BCs. Case of scalar-valued CDO-Vb schemes with a CO+ST algorithm. Predefined prototype to match the function pointer cs_cdo_enforce_bc_t. More...
void	cs_cdo_diffusion_svb_ocs_weak_dirichlet (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account Dirichlet BCs by a weak enforcement using Nitsche technique. Case of scalar-valued CDO-Vb schemes with an orthogonal splitting between the consistency/stabilization parts (OCS) Predefined prototype to match the function pointer cs_cdo_enforce_bc_t. More...
void	cs_cdo_diffusion_vvb_ocs_weak_dirichlet (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account Dirichlet BCs by a weak enforcement using Nitsche technique. A Dirichlet is set for the three components of the vector. Case of vector-valued CDO-Vb schemes with an orthogonal splitting between the consistency/stabilization parts (OCS) Predefined prototype to match the function pointer cs_cdo_enforce_bc_t. More...
void	cs_cdo_diffusion_vvb_ocs_sliding (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account a sliding BCs. Case of vector-valued CDO-Vb schemes with a OCS algorithm. Orthogonal splitting between Consistency/Stabilization parts. Predefined prototype to match the function pointer cs_cdo_enforce_bc_t. More...
void	cs_cdo_diffusion_svb_ocs_wsym_dirichlet (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account Dirichlet BCs by a weak enforcement using Nitsche technique plus a symmetric treatment. Case of CDO-Vb schemes with a COST/Bubble or Voronoi algorithm. One assumes an Orthogonal splitting between Consistency/Stabilization parts (OCS). Predefined prototype to match the function pointer cs_cdo_enforce_bc_t. More...
void	cs_cdo_diffusion_svb_wbs_robin (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account Robin BCs. Case of scalar-valued CDO-Vb schemes with a WBS algorithm. Predefined prototype to match the function pointer cs_cdo_enforce_bc_t. More...
void	cs_cdo_diffusion_svb_wbs_weak_dirichlet (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account Dirichlet BCs by a weak enforcement using Nitsche technique. Case of CDO-Vb schemes with a WBS algorithm. Predefined prototype to match the function pointer cs_cdo_enforce_bc_t. More...
void	cs_cdo_diffusion_svb_wbs_wsym_dirichlet (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account Dirichlet BCs by a weak enforcement using Nitsche technique plus a symmetric treatment. Case of CDO-Vb schemes with a WBS algorithm Predefined prototype to match the function pointer cs_cdo_enforce_bc_t. More...
void	cs_cdo_diffusion_vcb_weak_dirichlet (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account Dirichlet BCs by a weak enforcement using Nitsche technique. Case of CDO-VCb schemes with a WBS algorithm. Predefined prototype to match the function pointer cs_cdo_enforce_bc_t. More...
void	cs_cdo_diffusion_vcb_wsym_dirichlet (const cs_equation_param_t *eqp, const cs_cell_mesh_t *cm, cs_face_mesh_t *fm, cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_cell_sys_t *csys)
	Take into account Dirichlet BCs by a weak enforcement using Nitsche technique plus a symmetric treatment. Case of CDO-VCb schemes with a WBS algorithm Predefined prototype to match the function pointer cs_cdo_enforce_bc_t. More...
void	cs_cdo_diffusion_sfb_get_face_flux (const cs_cell_mesh_t *cm, const double *pot, const cs_hodge_t *hodge, cs_cell_builder_t *cb, double *flx)
	Compute the diffusive flux across primal faces for a given cell. Use the same consistent approximation as in the discrete Hodge op. for this computation. This function is dedicated to scalar-valued face-based schemes. Flux = -Consistent(Hdg) * GRAD(pot) Predefined prototype to match the function pointer cs_cdo_diffusion_cw_flux_t. More...
void	cs_cdo_diffusion_svb_get_dfbyc_flux (const cs_cell_mesh_t *cm, const double *pot, const cs_hodge_t *hodge, cs_cell_builder_t *cb, double *flx)
	Compute the diffusive flux across dual faces for a given cell. Use the same consistent approximation as in the discrete Hodge op. for this computation. This function is dedicated to vertex-based schemes. Flux = -Consistent(Hdg) * GRAD(pot) Predefined prototype to match the function pointer cs_cdo_diffusion_cw_flux_t. More...
void	cs_cdo_diffusion_svb_get_cell_flux (const cs_cell_mesh_t *cm, const double *pot, const cs_hodge_t *hodge, cs_cell_builder_t *cb, double *flx)
	Compute the constant approximation of the diffusive flux inside a (primal) cell. Use the same consistent approximation as in the discrete Hodge op. for this computation. This function is dedicated to vertex-based schemes. Flux = -Hdg * GRAD(pot) Predefined prototype to match the function pointer cs_cdo_diffusion_cw_flux_t. More...
void	cs_cdo_diffusion_svb_vbyf_flux (short int f, const cs_cell_mesh_t *cm, const cs_real_t *pot, const cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_real_t *flux)
	Compute the normal flux for a face assuming only the knowledge of the potential at cell vertices. Valid for algorithm relying on a spliting of the consistency/stabilization part as in OCS (also called CO+ST) or Bubble algorithm. This is used for reconstructing the normal flux from the degrees of freedom. The contribution for each vertex of the face is then computed. More...
void	cs_cdo_diffusion_wbs_get_dfbyc_flux (const cs_cell_mesh_t *cm, const cs_real_t *pot, const cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_real_t *flx)
	Compute the diffusive flux across dual faces for a given cell Use the WBS algo. for approximating the gradient The computation takes into account a subdivision into tetrahedra of the current cell based on p_{ef,c} Predefined prototype to match the function pointer cs_cdo_diffusion_cw_flux_t. More...
void	cs_cdo_diffusion_wbs_get_cell_flux (const cs_cell_mesh_t *cm, const cs_real_t *pot, const cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_real_t *flx)
	Compute the diffusive flux inside a given primal cell Use the WBS algo. for approximating the gradient The computation takes into account a subdivision into tetrahedra of the current cell based on p_{ef,c} Predefined prototype to match the function pointer cs_cdo_diffusion_cw_flux_t. More...
void	cs_cdo_diffusion_wbs_vbyf_flux (short int f, const cs_cell_mesh_t *cm, const cs_real_t *pot, const cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_real_t *flux)
	Compute the normal flux for a face assuming only the knowledge of the potential at cell vertices (and at cell center). WBS algorithm is used for reconstructing the normal flux from the degrees of freedom. More...
double	cs_cdo_diffusion_wbs_face_flux (const cs_face_mesh_t *fm, const cs_real_t pty_tens[3][3], const double *p_v, const double p_f, const double p_c, cs_cell_builder_t *cb)
	Compute the diffusive flux across a face (based on a subdivision into tetrahedra of the volume p_{f,c}) More...
void	cs_cdo_diffusion_sfb_cost_flux (short int f, const cs_cell_mesh_t *cm, const cs_real_t *pot, const cs_hodge_t *hodge, cs_cell_builder_t *cb, cs_real_t *flux)
	Compute the normal diffusive flux for a face assuming only the knowledge of the potential at faces and cell. CO+ST algorithm is used for reconstructing the normal flux from the degrees of freedom. More...
void	cs_cdovb_diffusion_p0_face_flux (const short int f, const cs_cell_mesh_t *cm, const cs_real_t diff_tensor[3][3], const cs_real_t *pot_values, cs_real_t *fluxes)
	Compute the normal flux for a face assuming only the knowledge of the potential at cell vertices. COST algorithm is used for reconstructing a piecewise constant gradient from the degrees of freedom. More...
void	cs_macfb_diffusion (const cs_cell_mesh_t *cm, const cs_macfb_builder_t *macb, const cs_property_t *diff_pty, cs_sdm_t *mat, cs_real_t *rhs)
	Compute the diffusion operator. More...

Detailed Description

Build discrete stiffness matrices and handled boundary conditions for diffusion term in CDO vertex-based and vertex+cell schemes.

Function Documentation

cs_cdo_diffusion_alge_block_dirichlet()

void cs_cdo_diffusion_alge_block_dirichlet	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account Dirichlet BCs by keeping the DoFs related to Dirichlet BCs in the algebraic system (i.e. a weak enforcement) The corresponding DoFs are algebraically "removed" of the system Block version.

| | | | | | | | | | | Aii | Aid | | Aii | 0 | |bi| |bi-Aid.xd | |---------—| --> |---------—| and |–| --> |-------—| | | | | | | | | | | | Adi | Add | | 0 | Id | |bd| | xd |

where xd is the value of the Dirichlet BC Predefined prototype to match the function pointer cs_cdo_enforce_bc_t

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cell-wise system

cs_cdo_diffusion_alge_dirichlet()

void cs_cdo_diffusion_alge_dirichlet	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account Dirichlet BCs by keeping the DoFs related to Dirichlet BCs in the algebraic system (i.e. a weak enforcement). The corresponding DoFs are algebraically "removed" of the system.

| | | | | | | | | | | Aii | Aid | | Aii | 0 | |bi| |bi-Aid.xd | |---------—| --> |---------—| and |–| --> |-------—| | | | | | | | | | | | Adi | Add | | 0 | Id | |bd| | xd |

where xd collects the values of the Dirichlet BC

Predefined prototype: function pointer cs_cdo_enforce_bc_t

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cell-wise system

cs_cdo_diffusion_alge_dirichlet_extra_block()

void cs_cdo_diffusion_alge_dirichlet_extra_block	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Function close to cs_cdo_diffusion_alge_dirichlet but dedicated to systems by blocks and especially for extra-diagonal blocks. The treatment of the RHS is a bit different.

Take into account Dirichlet BCs by keeping the DoFs related to Dirichlet BCs in the algebraic system (i.e. a weak enforcement). The corresponding DoFs are algebraically "removed" of the system

| | | | | | | | | | | Aii | Aid | | Aii | 0 | |bi| |bi-Aid.xd | |---------—| --> |---------—| and |–| --> |-------—| | | | | | | | | | | | Adi | Add | | 0 | 0 | |bd| | 0 |

where xd collects the values of the Dirichlet BC

Predefined prototype: function pointer cs_cdo_enforce_bc_t

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cell-wise system

cs_cdo_diffusion_pena_block_dirichlet()

void cs_cdo_diffusion_pena_block_dirichlet	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account Dirichlet BCs by a weak enforcement by a penalization technique with a huge value. Case of a cellwise system defined by block. Predefined prototype to match the function pointer cs_cdo_enforce_bc_t.

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cell-wise system

cs_cdo_diffusion_pena_dirichlet()

void cs_cdo_diffusion_pena_dirichlet	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account Dirichlet BCs by a weak enforcement by a penalization technique with a huge value. Predefined prototype to match the function pointer cs_cdo_enforce_bc_t.

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cell-wise system

cs_cdo_diffusion_sfb_cost_flux()

void cs_cdo_diffusion_sfb_cost_flux	(	short int	f,
		const cs_cell_mesh_t *	cm,
		const cs_real_t *	pot,
		const cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_real_t *	flux
	)

Compute the normal diffusive flux for a face assuming only the knowledge of the potential at faces and cell. CO+ST algorithm is used for reconstructing the normal flux from the degrees of freedom.

Parameters

[in]	f	face id in the cell mesh
[in]	cm	pointer to a cs_cell_mesh_t structure
[in]	pot	array of values of the potential (all the mesh)
[in]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	auxiliary structure dedicated to diffusion
[out]	flux	pointer to the value to set

cs_cdo_diffusion_sfb_cost_robin()

void cs_cdo_diffusion_sfb_cost_robin	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account Robin BCs. Case of scalar-valued CDO-Fb schemes with a CO+ST algorithm. Predefined prototype to match the function pointer cs_cdo_enforce_bc_t.

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cellwise system

cs_cdo_diffusion_sfb_get_face_flux()

void cs_cdo_diffusion_sfb_get_face_flux	(	const cs_cell_mesh_t *	cm,
		const double *	pot,
		const cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		double *	flx
	)

Compute the diffusive flux across primal faces for a given cell. Use the same consistent approximation as in the discrete Hodge op. for this computation. This function is dedicated to scalar-valued face-based schemes. Flux = -Consistent(Hdg) * GRAD(pot) Predefined prototype to match the function pointer cs_cdo_diffusion_cw_flux_t.

Parameters

[in]	cm	pointer to a cs_cell_mesh_t structure
[in]	pot	values of the potential fields at specific locations
[in]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	auxiliary structure for computing the flux
[in,out]	flx	values of the flux across primal faces

cs_cdo_diffusion_sfb_weak_dirichlet()

void cs_cdo_diffusion_sfb_weak_dirichlet	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account Dirichlet BCs by a weak enforcement using Nitsche technique. Case of scalar-valued CDO Face-based schemes Predefined prototype to match the function pointer cs_cdo_enforce_bc_t.

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cellwise system

cs_cdo_diffusion_sfb_wsym_dirichlet()

void cs_cdo_diffusion_sfb_wsym_dirichlet	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account Dirichlet BCs by a weak enforcement using Nitsche technique plus a symmetric treatment Case of scalar-valued CDO Face-based schemes Predefined prototype to match the function pointer cs_cdo_enforce_bc_t.

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cellwise system

cs_cdo_diffusion_svb_cost_robin()

void cs_cdo_diffusion_svb_cost_robin	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account Robin BCs. Case of scalar-valued CDO-Vb schemes with a CO+ST algorithm. Predefined prototype to match the function pointer cs_cdo_enforce_bc_t.

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cellwise system

cs_cdo_diffusion_svb_get_cell_flux()

void cs_cdo_diffusion_svb_get_cell_flux	(	const cs_cell_mesh_t *	cm,
		const double *	pot,
		const cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		double *	flx
	)

Compute the constant approximation of the diffusive flux inside a (primal) cell. Use the same consistent approximation as in the discrete Hodge op. for this computation. This function is dedicated to vertex-based schemes. Flux = -Hdg * GRAD(pot) Predefined prototype to match the function pointer cs_cdo_diffusion_cw_flux_t.

Parameters

[in]	cm	pointer to a cs_cell_mesh_t structure
[in]	pot	values of the potential fields at specific locations
[in]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	auxiliary structure for computing the flux
[in,out]	flx	values of the flux inside the cell

cs_cdo_diffusion_svb_get_dfbyc_flux()

void cs_cdo_diffusion_svb_get_dfbyc_flux	(	const cs_cell_mesh_t *	cm,
		const double *	pot,
		const cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		double *	flx
	)

Compute the diffusive flux across dual faces for a given cell. Use the same consistent approximation as in the discrete Hodge op. for this computation. This function is dedicated to vertex-based schemes. Flux = -Consistent(Hdg) * GRAD(pot) Predefined prototype to match the function pointer cs_cdo_diffusion_cw_flux_t.

Parameters

[in]	cm	pointer to a cs_cell_mesh_t structure
[in]	pot	values of the potential fields at specific locations
[in]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	auxiliary structure for computing the flux
[in,out]	flx	values of the flux across specific entities

cs_cdo_diffusion_svb_ocs_weak_dirichlet()

void cs_cdo_diffusion_svb_ocs_weak_dirichlet	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account Dirichlet BCs by a weak enforcement using Nitsche technique. Case of scalar-valued CDO-Vb schemes with an orthogonal splitting between the consistency/stabilization parts (OCS) Predefined prototype to match the function pointer cs_cdo_enforce_bc_t.

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cellwise system

cs_cdo_diffusion_svb_ocs_wsym_dirichlet()

void cs_cdo_diffusion_svb_ocs_wsym_dirichlet	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account Dirichlet BCs by a weak enforcement using Nitsche technique plus a symmetric treatment. Case of CDO-Vb schemes with a COST/Bubble or Voronoi algorithm. One assumes an Orthogonal splitting between Consistency/Stabilization parts (OCS). Predefined prototype to match the function pointer cs_cdo_enforce_bc_t.

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cellwise system

cs_cdo_diffusion_svb_vbyf_flux()

void cs_cdo_diffusion_svb_vbyf_flux	(	short int	f,
		const cs_cell_mesh_t *	cm,
		const cs_real_t *	pot,
		const cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_real_t *	flux
	)

Compute the normal flux for a face assuming only the knowledge of the potential at cell vertices. Valid for algorithm relying on a spliting of the consistency/stabilization part as in OCS (also called CO+ST) or Bubble algorithm. This is used for reconstructing the normal flux from the degrees of freedom. The contribution for each vertex of the face is then computed.

Parameters

[in]	f	face id in the cell mesh
[in]	cm	pointer to a cs_cell_mesh_t structure
[in]	pot	array of values of the potential (all the mesh)
[in]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	auxiliary structure for building the flux
[in,out]	flux	array of values to set (size: n_vc)

cs_cdo_diffusion_svb_wbs_robin()

void cs_cdo_diffusion_svb_wbs_robin	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account Robin BCs. Case of scalar-valued CDO-Vb schemes with a WBS algorithm. Predefined prototype to match the function pointer cs_cdo_enforce_bc_t.

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cellwise system

cs_cdo_diffusion_svb_wbs_weak_dirichlet()

void cs_cdo_diffusion_svb_wbs_weak_dirichlet	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account Dirichlet BCs by a weak enforcement using Nitsche technique. Case of CDO-Vb schemes with a WBS algorithm. Predefined prototype to match the function pointer cs_cdo_enforce_bc_t.

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cellwise system

cs_cdo_diffusion_svb_wbs_wsym_dirichlet()

void cs_cdo_diffusion_svb_wbs_wsym_dirichlet	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account Dirichlet BCs by a weak enforcement using Nitsche technique plus a symmetric treatment. Case of CDO-Vb schemes with a WBS algorithm Predefined prototype to match the function pointer cs_cdo_enforce_bc_t.

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cellwise system

cs_cdo_diffusion_vcb_weak_dirichlet()

void cs_cdo_diffusion_vcb_weak_dirichlet	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account Dirichlet BCs by a weak enforcement using Nitsche technique. Case of CDO-VCb schemes with a WBS algorithm. Predefined prototype to match the function pointer cs_cdo_enforce_bc_t.

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cellwise system

cs_cdo_diffusion_vcb_wsym_dirichlet()

void cs_cdo_diffusion_vcb_wsym_dirichlet	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account Dirichlet BCs by a weak enforcement using Nitsche technique plus a symmetric treatment. Case of CDO-VCb schemes with a WBS algorithm Predefined prototype to match the function pointer cs_cdo_enforce_bc_t.

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cellwise system

cs_cdo_diffusion_vfb_weak_dirichlet()

void cs_cdo_diffusion_vfb_weak_dirichlet	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account Dirichlet BCs by a weak enforcement using Nitsche technique. Case of vector-valued CDO Face-based schemes The idea is to compute the scalar version and dispatch it three times, one for each Cartesian components Predefined prototype to match the function pointer cs_cdo_enforce_bc_t.

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cellwise system

cs_cdo_diffusion_vfb_wsym_dirichlet()

void cs_cdo_diffusion_vfb_wsym_dirichlet	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account Dirichlet BCs by a weak enforcement using Nitsche technique plus a symmetric treatment. Case of vector-valued CDO Face-based schemes The idea is to compute the scalar version and dispatch it three times, one for each Cartesian components Predefined prototype to match the function pointer cs_cdo_enforce_bc_t.

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cellwise system

cs_cdo_diffusion_vfb_wsym_sliding()

void cs_cdo_diffusion_vfb_wsym_sliding	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account sliding BCs by a weak enforcement using Nitsche technique plus a symmetric treatment. Case of vector-valued CDO Face-based schemes Predefined prototype to match the function pointer cs_cdo_enforce_bc_t.

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cellwise system

cs_cdo_diffusion_vvb_ocs_sliding()

void cs_cdo_diffusion_vvb_ocs_sliding	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account a sliding BCs. Case of vector-valued CDO-Vb schemes with a OCS algorithm. Orthogonal splitting between Consistency/Stabilization parts. Predefined prototype to match the function pointer cs_cdo_enforce_bc_t.

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cellwise system

cs_cdo_diffusion_vvb_ocs_weak_dirichlet()

void cs_cdo_diffusion_vvb_ocs_weak_dirichlet	(	const cs_equation_param_t *	eqp,
		const cs_cell_mesh_t *	cm,
		cs_face_mesh_t *	fm,
		cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_cell_sys_t *	csys
	)

Take into account Dirichlet BCs by a weak enforcement using Nitsche technique. A Dirichlet is set for the three components of the vector. Case of vector-valued CDO-Vb schemes with an orthogonal splitting between the consistency/stabilization parts (OCS) Predefined prototype to match the function pointer cs_cdo_enforce_bc_t.

Parameters

[in]	eqp	pointer to a cs_equation_param_t struct.
[in]	cm	pointer to a cs_cell_mesh_t structure
[in,out]	fm	pointer to a cs_face_mesh_t structure
[in,out]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	pointer to a cs_cell_builder_t structure
[in,out]	csys	structure storing the cellwise system

cs_cdo_diffusion_wbs_face_flux()

double cs_cdo_diffusion_wbs_face_flux	(	const cs_face_mesh_t *	fm,
		const cs_real_t	pty_tens[3][3],
		const double *	p_v,
		const double	p_f,
		const double	p_c,
		cs_cell_builder_t *	cb
	)

Compute the diffusive flux across a face (based on a subdivision into tetrahedra of the volume p_{f,c})

Parameters

[in]	fm	pointer to a cs_face_mesh_t structure
[in]	pty_tens	3x3 matrix related to the diffusion property
[in]	p_v	array of values attached to face vertices
[in]	p_f	value attached to the face
[in]	p_c	value attached to the cell
[in,out]	cb	auxiliary structure dedicated to diffusion

Returns

the value of the diffusive flux across the current face

cs_cdo_diffusion_wbs_get_cell_flux()

void cs_cdo_diffusion_wbs_get_cell_flux	(	const cs_cell_mesh_t *	cm,
		const cs_real_t *	pot,
		const cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_real_t *	flx
	)

Compute the diffusive flux inside a given primal cell Use the WBS algo. for approximating the gradient The computation takes into account a subdivision into tetrahedra of the current cell based on p_{ef,c} Predefined prototype to match the function pointer cs_cdo_diffusion_cw_flux_t.

Parameters

[in]	cm	pointer to a cs_cell_mesh_t structure
[in]	pot	values of the potential fields at vertices
[in]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	auxiliary structure for computing the flux
[in,out]	flx	flux vector inside this cell

cs_cdo_diffusion_wbs_get_dfbyc_flux()

void cs_cdo_diffusion_wbs_get_dfbyc_flux	(	const cs_cell_mesh_t *	cm,
		const cs_real_t *	pot,
		const cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_real_t *	flx
	)

Compute the diffusive flux across dual faces for a given cell Use the WBS algo. for approximating the gradient The computation takes into account a subdivision into tetrahedra of the current cell based on p_{ef,c} Predefined prototype to match the function pointer cs_cdo_diffusion_cw_flux_t.

Parameters

[in]	cm	pointer to a cs_cell_mesh_t structure
[in]	pot	values of the potential fields at vertices
[in]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	auxiliary structure for computing the flux
[in,out]	flx	flux across dual faces inside this cell

cs_cdo_diffusion_wbs_vbyf_flux()

void cs_cdo_diffusion_wbs_vbyf_flux	(	short int	f,
		const cs_cell_mesh_t *	cm,
		const cs_real_t *	pot,
		const cs_hodge_t *	hodge,
		cs_cell_builder_t *	cb,
		cs_real_t *	flux
	)

Compute the normal flux for a face assuming only the knowledge of the potential at cell vertices (and at cell center). WBS algorithm is used for reconstructing the normal flux from the degrees of freedom.

Parameters

[in]	f	face id in the cell mesh
[in]	cm	pointer to a cs_cell_mesh_t structure
[in]	pot	array of values of the potential (all the mesh)
[in]	hodge	pointer to a cs_hodge_t structure
[in,out]	cb	auxiliary structure dedicated to diffusion
[in,out]	flux	array of values to set (size: n_vc)

cs_cdovb_diffusion_p0_face_flux()

void cs_cdovb_diffusion_p0_face_flux	(	const short int	f,
		const cs_cell_mesh_t *	cm,
		const cs_real_t	diff_tensor[3][3],
		const cs_real_t *	pot_values,
		cs_real_t *	fluxes
	)

Compute the normal flux for a face assuming only the knowledge of the potential at cell vertices. COST algorithm is used for reconstructing a piecewise constant gradient from the degrees of freedom.

Parameters

[in]	f	face id in the cell mesh
[in]	cm	pointer to a cs_cell_mesh_t structure
[in]	diff_tensor	property tensor times the face normal
[in]	pot_values	array of values of the potential (all the mesh)
[in,out]	fluxes	values of the fluxes related to each vertex

cs_macfb_diffusion()

void cs_macfb_diffusion	(	const cs_cell_mesh_t *	cm,
		const cs_macfb_builder_t *	macb,
		const cs_property_t *	diff_pty,
		cs_sdm_t *	mat,
		cs_real_t *	rhs
	)

Compute the diffusion operator.

Compute the diffusion operator for the MAC face-based scheme.

Parameters

[in]	cm	pointer to a cs_cell_mesh_t structure
[in]	macb	pointer to a cs_macfb_builder_t structure
[in]	diff_pty	pointer to a cs_property_t structure
[in,out]	mat	pointer to a cs_sdm_t structure. It is filled inside the function. Have to preallocated.
[in,out]	rhs	pointer to a cs_real_t array. It is filled inside the function. Have to preallocated.