conserving.h File Reference

Go to the source code of this file.

Functions
static void	momentum_refine (Point point, scalar u)
static void	momentum_restriction (Point point, scalar u)
void	event_defaults (void)
	We switch-off the default advection scheme of the centered solver.
void	event_stability (void) dtmax
	We need to overload the stability event so that the CFL is taken into account (because we set stokes to true).
	for (int _d=0;_d< 2;_d++) static double boundary_q1_x(Point neighbor
	We will transport the two components of the momentum, \(q_1=f \rho_1 \mathbf{u}\) and \(q_2=(1 - f) \rho_2 \mathbf{u}\).
void	event_vof (void)
	Event: vof (i++)
void	event_tracer_advection (void)
	We set the list of interfaces back to its default value.

Variables
Point	point
Point scalar	q1
Point scalar bool *	data
Point scalar	q2
static scalar *	interfaces1 = NULL
	We overload the vof() event to transport consistently the volume fraction and the momentum of each phase.

Function Documentation

event_defaults()

void event_defaults

(

void

)

We switch-off the default advection scheme of the centered solver.

Event: defaults (i = 0)

On trees, the refinement and restriction functions above rely on the volume fraction field f being refined/restricted before the components of velocity. To ensure this, we move f to the front of the field list (all).

We then set the refinement and restriction functions for the components of the velocity field. The boundary conditions on \(\mathbf{u}\) now depend on those on \(f\).

Definition at line 40 of file conserving.h.

References all, dimension, f, scalar::i, i, list_add(), momentum_refine(), momentum_restriction(), stokes, u, and x.

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event_stability()

void event_stability

(

void

)

We need to overload the stability event so that the CFL is taken into account (because we set stokes to true).

Event: stability (i++)

We need to overload the stability event so that the CFL is taken into account (because we set stokes to true).

We need to overload the stability event so that the CFL is taken into account (because we set stokes to true).

Time step restriction based on the speed of sound

We need to overload the stability event so that the CFL is taken into account (because we set stokes to true).

Stability condition

The surface tension scheme is time-explicit so the maximum timestep is the oscillation period of the smallest capillary wave.

\[ T = \sqrt{\frac{\rho_{m}\Delta_{min}^3}{\pi\sigma}} \]

with \(\rho_m=(\rho_1+\rho_2)/2.\) and \(\rho_1\), \(\rho_2\) the densities on either side of the interface.

We need to overload the stability event so that the CFL is taken into account (because we set stokes to true).

Stability condition

The surface tension scheme is time-explicit so the maximum timestep is the oscillation period of the smallest capillary wave.

\[ T = \sqrt{\frac{\rho_{m}\Delta_{min}^3}{\pi\sigma}} \]

with \(\rho_m=(\rho_1+\rho_2)/2.\) and \(\rho_1\), \(\rho_2\) the densities on either side of the interface.

We need to overload the stability event so that the CFL is taken into account (because we set stokes to true).

Event: stability (i++)

We first compute the minimum and maximum values of \(\alpha/f_m = 1/\rho\), as well as \(\Delta_{min}\).

The maximum timestep is set using the sum of surface tension coefficients.

We first compute the minimum and maximum values of \(\alpha/f_m = 1/\rho\), as well as \(\Delta_{min}\).

The maximum timestep is set using the sum of surface tension coefficients.

Definition at line 110 of file all-mach.h.

References _i, alpha, c, CFL, CFLa, CFLac, cube(), d, dmin, dry, dt, dtmax, dtnext(), fm, G, h, HUGE, max, min, pi, point, sigma, sound_speed(), stokes, timestep(), u, uf, vector::x, and x.

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event_tracer_advection()

void event_tracer_advection

(

void

)

We set the list of interfaces back to its default value.

Event: tracer_advection (i++)

Definition at line 198 of file conserving.h.

References interfaces, and interfaces1.

event_vof()

void event_vof

(

void

)

Event: vof (i++)

We allocate two temporary vector fields to store the two components of the momentum and set the boundary conditions and prolongation functions. The boundary conditions on \(q_1\) and \(q_2\) depend on the boundary conditions on \(f\).

We split the total momentum \(q\) into its two components \(q1\) and \(q2\) associated with \(f\) and \(1 - f\) respectively.

Momentum \(q2\) is associated with \(1 - f\), so we set the inverse attribute to true. We use the same slope-limiting as for the velocity field.

We associate the transport of \(q1\) and \(q2\) with \(f\) and transport all fields consistently using the VOF scheme.

We recover the advected velocity field using the total momentum and the density

We set the list of interfaces to NULL so that the default vof() event does nothing (otherwise we would transport \(f\) twice).

Definition at line 122 of file conserving.h.

References _i, clamp(), dimension, f, free(), scalar::i, i, interfaces, interfaces1, list_add(), list_concat(), nboundary, q1, q2, rho, rho1, rho2, s, tracers, u, vof_advection(), and x.

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for()

for

(

)

We will transport the two components of the momentum, \(q_1=f \rho_1 \mathbf{u}\) and \(q_2=(1 - f) \rho_2 \mathbf{u}\).

Similarly, on trees we need prolongation functions which also follow this definition.

We will need to impose boundary conditions which match this definition. This is done using the functions below.

momentum_refine()

static void momentum_refine ( Point  point, scalar  u  )

static

Momentum-conserving advection of velocity

This file implements momentum-conserving VOF advection of the velocity components for the two-phase Navier–Stokes solver.

On trees, we first define refinement and restriction functions which guarantee conservation of each component of the total momentum. Note that these functions do not guarantee conservation of momentum for each phase.

Definition at line 16 of file conserving.h.

References cm, dimension, f, point, refine_bilinear(), rho, SEPS, u, and x.

Referenced by event_defaults().

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momentum_restriction()

static void momentum_restriction ( Point  point, scalar  u  )

static

Definition at line 26 of file conserving.h.

References cm, dimension, f, rho, SEPS, u, and x.

Referenced by event_defaults().

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Variable Documentation

data

Point scalar bool * data

Initial value:

{
  return clamp(f[],0.,1.)*rho1*u.x[]

Definition at line 86 of file conserving.h.

interfaces1

scalar* interfaces1 = NULL

static

We overload the vof() event to transport consistently the volume fraction and the momentum of each phase.

Definition at line 119 of file conserving.h.

Referenced by event_tracer_advection(), and event_vof().

point

Point point

Definition at line 86 of file conserving.h.

Referenced by adapt_wavelet(), advance_saint_venant(), advect(), alloc_children(), allocated(), balance(), box_boundary_level(), box_boundary_level(), box_boundary_level(), box_boundary_level_normal(), box_boundary_level_normal(), box_boundary_level_tangent(), centroids_curvature_fit(), check_two_one(), coarsen_cell(), coarsen_cell_recursive(), compile_expression(), curvature(), dirichlet(), dirichlet_gradient(), distance(), embed_area_center(), embed_flux(), embed_force(), embed_fraction_refine(), embed_geometry(), embed_gradient(), embed_vorticity(), evaluate_expression(), event_acceleration(), event_pressure(), event_properties(), event_stability(), event_viscous_term(), face_fraction(), facet_normal(), fE_refine(), for(), foreach(), foreach_boundary_dir(), foreach_cell_post_root(), foreach_child(), foreach_face_generic(), foreach_level_stencil(), foreach_mem(), foreach_neighbor(), foreach_slice_x(), foreach_slice_y(), foreach_stencil(), foreach_stencil_generic(), foreach_tree(), foreach_visible(), fraction_refine(), glvertex_normal3d(), height_curvature(), height_curvature_fit(), height_myc_normal(), height_normal(), height_position(), heights(), if(), increment_neighbors(), init_grid(), input_gfs(), interface_area(), interface_normal(), interp(), interpolate(), interpolate_array(), inverse_wavelet(), is_local_prolongation(), is_refined_check(), locals_pids(), locate(), locate(), matrix(), mg_cycle(), momentum_refine(), mpi_boundary_coarsen(), mpi_boundary_refine(), mpi_boundary_update_buffers(), msolve(), multigrid_debug(), multigrid_restriction(), neighbor(), neumann(), no_coalescence(), normal_neighbor(), OMP_PARALLEL(), output_tree(), periodic_boundary_level_x(), POINT_VARIABLES(), prolongation_elevation(), rcv_append(), rcv_pid_append(), reconstruction(), recursive(), refine(), refine_bilinear(), refine_biquadratic(), refine_cell(), refine_cm_axi(), refine_distance(), refine_face(), refine_face_solenoidal(), refine_face_x_axi(), refine_level(), refine_linear(), relax(), relax_diffusion(), relax_GN(), relax_hydro(), relax_nh(), relax_nh(), relax_viscosity(), residual(), residual_diffusion(), residual_nh(), residual_nh(), residual_nh3(), restore_mpi(), restriction_embed_linear(), restriction_face(), segment_flux(), solve(), terrain(), tree_boundary_level(), unrefine(), update_cache_f(), update_distance(), val(), VARIABLES(), vertical_diffusion(), vertical_remapping(), vertical_velocity(), vof_concentration_refine(), and wavelet().

q1

scalar q1

Initial value:

{
  for (int _c = 0; _c < 4; _c++) 
    q1[] = clamp(f[],0.,1.)*rho1*u.x[]

Definition at line 86 of file conserving.h.

Referenced by event_vof().

q2

scalar q2

Initial value:

{
  for (int _c = 0; _c < 4; _c++) 
    q2[] = (1. - clamp(f[],0.,1.))*rho2*u.x[]

Definition at line 92 of file conserving.h.

Referenced by event_vof().