#include "poisson.h"

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Macros
#define	NH 1

#define	PHIT 6.

Functions
void	event_defaults (void)
	Event: defaults (i = 0)

void	correct_qz (double dt, const scalar phis)

void	event_viscous_term (void)
	Event: viscous_term (i++)

static void	coeffs1 (Point point, scalar hl, double a, double(b)[2], double c)

static void	coeffs2 (Point point, scalar hl, double a, double(b)[2], double c)

static void	matrix (Point point, scalar phil, scalar rhsl, double a, double b, double c, double d)

static void	matrix1 (Point point, scalar phil, scalar rhsl, double a, double b, double c, double d)

static trace void	relax_nh (scalar phil, scalar rhsl, int lev, void *data)

static double	residual_nh (scalar phil, scalar rhsl, scalar resl, void data)

static trace void	relax_nh1 (scalar phil, scalar rhsl, int lev, void *data)

static double	residual_nh2 (scalar phil, scalar rhsl, scalar resl, void data)

static double	residual_nh3 (scalar phil, scalar rhsl, scalar resl, void data)

void	event_pressure (void)
	Event: pressure (i++)

void	event_cleanup (void)
	Event: cleanup (i = end, last)

Variables
scalar *	qzl = NULL

scalar *	phil = NULL

mgstats	mgp

double *	alpha = NULL

double *	gammap = NULL

scalar	phit = zeroc

Macro Definition Documentation

◆ NH

#define NH 1

The vertically-staggered non-hydrostatic solver

See section 3.6.1 of Popinet (2019). Note that this uses the vertical momentum qz rather than vertical velocity w and will not be compatible with [hydro.h]().

Definition at line 10 of file nh-staggered.h.

◆ PHIT

#define PHIT 6.

Definition at line 189 of file nh-staggered.h.

Function Documentation

◆ coeffs1()

static void coeffs1	(	Point	point,
		scalar *	hl,
		double *	a,
		double(*)	b[2],
		double *	c
	)

static

Definition at line 250 of file nh-staggered.h.

References a, b, c, h, l, nl, PHIT, x, and zb.

Referenced by event_pressure(), and matrix().

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◆ coeffs2()

static void coeffs2	(	Point	point,
		scalar *	hl,
		double *	a,
		double(*)	b[2],
		double *	c
	)

static

Definition at line 274 of file nh-staggered.h.

References a, b, c, h, l, nl, PHIT, and x.

Referenced by matrix().

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◆ correct_qz()

void correct_qz	(	double	dt,
		const scalar	phis
	)

Definition at line 191 of file nh-staggered.h.

References _i, alpha, dt, h, l, nl, phi, phil, PHIT, phit, qzl, s, sq(), and x.

Referenced by event_pressure(), and event_viscous_term().

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◆ event_cleanup()

void event_cleanup ( void )

Event: cleanup (i = end, last)

Definition at line 693 of file nh-staggered.h.

References alpha, free(), gammap, phil, qzl, and x.

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◆ event_defaults()

void event_defaults ( void )

Event: defaults (i = 0)

Boundary conditions for VOF-advected tracers usually depend on boundary conditions for the VOF field.

Event: defaults (i = 0)

Initialisation

We set the default values.

Electrohydrodynamic stresses

The EHD force density, \(\mathbf{f}_e\), can be computed as the divergence of the Maxwell stress tensor \(\mathbf{M}\),

\[ M_{ij} = \varepsilon (E_i E_j - \frac{E^2}{2}\delta_{ij}) \]

where \(E_i\) is the \(i\)-component of the electric field, \(\mathbf{E}=-\nabla \phi\) and \(\delta_{ij}\) is the Kronecker delta.

We need to add the corresponding acceleration to the Navier–Stokes solver.

If the acceleration vector a (defined by the Navier–Stokes solver) is constant, we make it variable.

Event: defaults (i = 0)

Event: defaults (i = 0 )

Defaults

On trees we need to ensure conservation of the tracer when refining/coarsening.

Event: defaults (i = 0)

it is an acceleration. If necessary, we allocate a new vector field to store it.

Event: defaults (i = 0)

\[ \begin{aligned} 0 & = - \sum_k \nabla \cdot [\theta_H (hu)_k^{n + 1} + (1 - \theta_H) (hu)^n_k] \\ \frac{(hu)^{n + 1}_k - (hu)_k^n}{\Delta t} & = - \Delta tgh^{n + 1 / 2}_k (\theta_H \nabla \eta_r^{n + 1} + (1 - \theta_H) \nabla \eta_r^n) \end{aligned} \]

where \(\eta_r\) is the equivalent free-surface height (i.e. pressure) applied on the rigid lid.

Event: defaults (i = 0)

The default density field is set to unity (times the metric).

We reset the multigrid parameters to their default values.

If the viscosity is non-zero, we need to allocate the face-centered viscosity field.

We also initialize the list of tracers to be advected with the VOF function \(f\) (or its complementary function).

We set limiting.

On trees, we ensure that limiting is also applied to prolongation and refinement.

We add the interface and the density to the default display.

We switch to a pure minmod limiter by default for increased robustness.

With the MUSCL scheme we use the CFL depends on the dimension of the problem.

On trees we need to replace the default bilinear refinement/prolongation with linear so that reconstructed values also use slope limiting.

The restriction/refine attributes of the charge density are those of a tracer otherwise the conservation is not guaranteed.

By default the permittivity is unity and other quantities are zero.

The (velocity) CFL is limited by the unsplit advection scheme, so is dependent on the dimension. The (gravity wave) CFL is set to 1/2 (if not already set by the user).

The gradient and prolongation/restriction functions are set for all tracer fields.

We setup the default display.

Definition at line 20 of file nh-staggered.h.

References alpha, assert, beta, calloc(), gammap, l, list_append(), nl, phi, phil, qzl, reset, tracers, and x.