Poisson and diffusion solvers. More...

Functions
void	gfs_multilevel_params_write (GfsMultilevelParams par, FILE fp)
void	gfs_multilevel_params_stats_write (GfsMultilevelParams par, FILE fp)
GfsLinearProblem *	gfs_linear_problem_new (GfsDomain *domain)
void	gfs_linear_problem_add_stencil (GfsLinearProblem lp, GfsStencil stencil)
void	gfs_linear_problem_destroy (GfsLinearProblem *lp)
GfsLinearProblem *	gfs_get_poisson_problem (GfsDomain domain, GfsVariable rhs, GfsVariable lhs, GfsVariable dia, gint maxlevel, GfsVariable *v)
void	gfs_relax (GfsDomain domain, guint d, gint max_depth, gdouble omega, GfsVariable u, GfsVariable rhs, GfsVariable dia)
void	gfs_residual (GfsDomain domain, guint d, FttTraverseFlags flags, gint max_depth, GfsVariable u, GfsVariable rhs, GfsVariable dia, GfsVariable *res)
void	gfs_poisson_coefficients (GfsDomain domain, GfsFunction alpha, gboolean positive, gboolean centered, gboolean reset)
void	gfs_source_tension_coefficients (GfsSourceTension s, GfsDomain domain, GfsFunction *alpha)
void	gfs_poisson_cycle (GfsDomain domain, GfsMultilevelParams p, GfsVariable u, GfsVariable rhs, GfsVariable dia, GfsVariable res)
gdouble	gfs_poisson_compatibility (GfsDomain domain, GfsVariable lhs, GfsVariable *rhs, gdouble dt)
void	gfs_poisson_solve (GfsDomain domain, GfsMultilevelParams par, GfsVariable lhs, GfsVariable rhs, GfsVariable res, GfsVariable dia, gdouble dt)
void	gfs_diffusion_coefficients (GfsDomain domain, GfsSourceDiffusion d, gdouble dt, GfsVariable rhoc, GfsVariable metric, GfsFunction *alpha, gdouble beta)
void	gfs_diffusion_rhs (GfsDomain domain, GfsVariable v, GfsVariable rhs, GfsVariable rhoc, GfsVariable *metric, gdouble beta)
void	gfs_diffusion_residual (GfsDomain domain, GfsVariable u, GfsVariable rhs, GfsVariable rhoc, GfsVariable metric, GfsVariable res)
void	gfs_diffusion_cycle (GfsDomain domain, guint levelmin, guint depth, guint nrelax, GfsVariable u, GfsVariable rhs, GfsVariable rhoc, GfsVariable metric, GfsVariable res)
GfsLinearProblem *	gfs_get_diffusion_problem (GfsDomain domain, GfsVariable rhs, GfsVariable lhs, GfsVariable rhoc, GfsVariable metric, gint maxlevel, GfsVariable v)

Detailed Description

Poisson and diffusion solvers.

Function Documentation

void gfs_diffusion_coefficients	(	GfsDomain *	domain,
		GfsSourceDiffusion *	d,
		gdouble	dt,
		GfsVariable *	rhoc,
		GfsVariable *	metric,
		GfsFunction *	alpha,
		gdouble	beta
	)

Parameters:

domain	a #GfsDomain.
d	a #GfsSourceDiffusion.
dt	the time-step.
rhoc	where to store the mass.
metric	where to store the implicit metric term (or NULL).
alpha	the inverse of density or NULL.
beta	the implicitness parameter (0.5 Crank-Nicholson, 1. backward Euler).

Initializes the face coefficients for the diffusion equation.

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void gfs_diffusion_cycle	(	GfsDomain *	domain,
		guint	levelmin,
		guint	depth,
		guint	nrelax,
		GfsVariable *	u,
		GfsVariable *	rhs,
		GfsVariable *	rhoc,
		GfsVariable *	metric,
		GfsVariable *	res
	)

Parameters:

domain	the domain on which to solve the diffusion equation.
levelmin	the top level of the multigrid hierarchy.
depth	the total depth of the domain.
nrelax	the number of relaxations to apply at each level.
u	the variable to use as left-hand side.
rhs	the right-hand side.
rhoc	the mass.
metric	the metric term.
res	the residual.

Apply one multigrid iteration to the diffusion equation for u.

The initial value of res on the leaves of root must be set to the residual of the diffusion equation using gfs_diffusion_residual().

The diffusion coefficients must be set using gfs_diffusion_coefficients().

The values of u on the leaf cells are updated as well as the values of res (i.e. the cell tree is ready for another iteration).

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void gfs_diffusion_residual	(	GfsDomain *	domain,
		GfsVariable *	u,
		GfsVariable *	rhs,
		GfsVariable *	rhoc,
		GfsVariable *	metric,
		GfsVariable *	res
	)

Parameters:

domain	a #GfsDomain.
u	the variable to use as left-hand side.
rhs	the right-hand side.
rhoc	the mass.
metric	the metric term.
res	the residual.

Sets the res variable of each leaf cell of domain to the residual of the diffusion equation for v.

The diffusion coefficients must have been set using gfs_diffusion_coefficients() and the right-hand side using gfs_diffusion_rhs().

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void gfs_diffusion_rhs	(	GfsDomain *	domain,
		GfsVariable *	v,
		GfsVariable *	rhs,
		GfsVariable *	rhoc,
		GfsVariable *	metric,
		gdouble	beta
	)

Parameters:

domain	a #GfsDomain.
v	a #GfsVariable.
rhs	a #GfsVariable.
rhoc	the mass.
metric	the metric term.
beta	the implicitness parameter (0.5 Crank-Nicholson, 1. backward Euler).

Adds to the rhs variable of cell the right-hand side of the diffusion equation for variable v.

The diffusion coefficients must have been already set using gfs_diffusion_coefficients().

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GfsLinearProblem* gfs_get_diffusion_problem	(	GfsDomain *	domain,
		GfsVariable *	rhs,
		GfsVariable *	lhs,
		GfsVariable *	rhoc,
		GfsVariable *	metric,
		gint	maxlevel,
		GfsVariable *	v
	)

Parameters:

domain	the domain over which the poisson problem is defined
rhs	the variable to use as right-hand side
lhs	the variable to use as left-hand side
rhoc	the mass.
metric	the metric term (or NULL).
maxlevel	the maximum level to consider (or -1).
v	a #GfsVariable of which lhs is an homogeneous version.

Extracts the diffusion problem associated with lhs and rhs.

Returns:: a #GfsLinearProblem.

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GfsLinearProblem* gfs_get_poisson_problem	(	GfsDomain *	domain,
		GfsVariable *	rhs,
		GfsVariable *	lhs,
		GfsVariable *	dia,
		gint	maxlevel,
		GfsVariable *	v
	)

Parameters:

domain	the domain over which the poisson problem is defined
rhs	the variable to use as right-hand side
lhs	the variable to use as left-hand side
dia	the diagonal weight
maxlevel	the maximum level to consider (or -1).
v	a #GfsVariable of which lhs is an homogeneous version.

Extracts the poisson problem associated with lhs and rhs.

Returns:: a #GfsLinearProblem.

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void gfs_linear_problem_add_stencil	(	GfsLinearProblem *	lp,
		GfsStencil *	stencil
	)

Parameters:

lp	a #GfsLinearProblem.
stencil	a #GfsStencil.

Adds a stencil to the linear problem.

void gfs_linear_problem_destroy ( GfsLinearProblem * lp )

Parameters:

lp	a #GfsLinearProblem.

Destroys a #GfsLinearProblem.

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GfsLinearProblem* gfs_linear_problem_new ( GfsDomain * domain )

Parameters:

domain a #GfsDomain.

Returns:: a new #GfsLinearProblem.

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void gfs_multilevel_params_stats_write	(	GfsMultilevelParams *	par,
		FILE *	fp
	)

Parameters:

par	the multilevel parameters.
fp	a file pointer.

Writes in fp the statistics contained in p.

void gfs_multilevel_params_write	(	GfsMultilevelParams *	par,
		FILE *	fp
	)

Parameters:

par	the multilevel parameters.
fp	a file pointer.

Writes in fp a text representation of the multilevel parameters par.

void gfs_poisson_coefficients	(	GfsDomain *	domain,
		GfsFunction *	alpha,
		gboolean	positive,
		gboolean	centered,
		gboolean	reset
	)

Parameters:

domain	a #GfsDomain.
alpha	the inverse of density or NULL.
positive	if TRUE, alpha must be strictly positive.
centered	TRUE if solving for a centered variable.
reset	TRUE if resetting previous coefficients.

Initializes the face coefficients for the Poisson equation $\nabla\cdot\alpha\nabla p=\dots$ .

If alpha is NULL, it is taken to be unity.

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gdouble gfs_poisson_compatibility	(	GfsDomain *	domain,
		GfsVariable *	lhs,
		GfsVariable *	rhs,
		gdouble	dt
	)

Parameters:

domain	the domain over which the poisson problem is solved.
lhs	the variable to use as left-hand side.
rhs	the variable to use as right-hand side.
dt	the timestep.

Returns:: the absolute value of the compatibility condition for a Poisson equation using lhs as left-hand-side and rhs as right-hand-side.

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void gfs_poisson_cycle	(	GfsDomain *	domain,
		GfsMultilevelParams *	p,
		GfsVariable *	u,
		GfsVariable *	rhs,
		GfsVariable *	dia,
		GfsVariable *	res
	)

Parameters:

domain	the domain on which to solve the Poisson equation.
p	the #GfsMultilevelParams.
u	the variable to use as left-hand side.
rhs	the variable to use as right-hand side.
dia	the diagonal weight.
res	the residual.

Apply one multigrid iteration to the Poisson equation defined by u and rhs.

The initial value of res on the leaves of root must be set to the residual of the Poisson equation (using gfs_residual()).

The face coefficients must be set using gfs_poisson_coefficients().

The values of u on the leaf cells are updated as well as the values of res (i.e. the cell tree is ready for another iteration).

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void gfs_poisson_solve	(	GfsDomain *	domain,
		GfsMultilevelParams *	par,
		GfsVariable *	lhs,
		GfsVariable *	rhs,
		GfsVariable *	res,
		GfsVariable *	dia,
		gdouble	dt
	)

Parameters:

domain	the domain over which the poisson problem is solved.
par	the parameters of the poisson problem.
lhs	the variable to use as left-hand side.
rhs	the variable to use as right-hand side.
res	the variable in which to store the residual
dia	the diagonal weight.
dt	the length of the time-step.

Solves the poisson problem over domain using Gerris' native multigrid poisson solver.

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void gfs_relax	(	GfsDomain *	domain,
		guint	d,
		gint	max_depth,
		gdouble	omega,
		GfsVariable *	u,
		GfsVariable *	rhs,
		GfsVariable *	dia
	)

Parameters:

domain	the domain to relax.
d	number of dimensions (2 or 3).
max_depth	the maximum depth of the domain to relax.
omega	the over-relaxation parameter.
u	the variable to use as left-hand side.
rhs	the variable to use as right-hand side.
dia	the diagonal weight.

Apply one pass of a Jacobi relaxation to all the leaf cells of domain with a level inferior or equal to max_depth and to all the cells at level max_depth. The relaxation should converge (if the right-hand-side rhs verifies the solvability conditions) toward the solution of a Poisson equation for u at the maximum depth.

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void gfs_residual	(	GfsDomain *	domain,
		guint	d,
		FttTraverseFlags	flags,
		gint	max_depth,
		GfsVariable *	u,
		GfsVariable *	rhs,
		GfsVariable *	dia,
		GfsVariable *	res
	)

Parameters:

domain	a domain.
d	number of dimensions (2 or 3).
flags	which types of cells are to be visited.
max_depth	maximum depth of the traversal.
u	the variable to use as left-hand side.
rhs	the variable to use as right-hand side.
dia	the diagonal weight.
res	the variable to use to store the residual.

For each cell of domain, computes the sum of the residual over the volume of the cell for a Poisson equation with u as left-hand-side and rhs as right-hand-side. Stores the result in res.

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void gfs_source_tension_coefficients	(	GfsSourceTension *	s,
		GfsDomain *	domain,
		GfsFunction *	alpha
	)

Parameters:

s	a #GfsSourceTension.
domain	a #GfsDomain.
alpha	the inverse of density or NULL.

Initializes the face coefficients with the surface tension term (interface curvature times surface tension coefficient).

If alpha is NULL, it is taken to be unity.

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poisson.c File Reference

Functions

Detailed Description

Function Documentation