Classes
class	SolveWatch

Functions
	all_fluid (n)

	scene_slab (n)

	scene_tilted (n, mx=0.6, my=-0.5, mz=0.62456)

	_plic_volume (mx, my, mz, alpha)

	scene_droplet (n, r=None)

	make_solver (n, C, rho_g, rho_l, mu, dt, U, momentum, rho0=None)

	uniform_error (s, U)

	gate_uniform (n=32, steps=200, scenes=("tilted",), ratios=(10.0, 1e2, 1e3, 1e4))

	gate_uniform_advection_only (n=32, steps=1, ratios=(10.0, 1e2, 1e3, 1e4))

	gate_single_phase (n=32, steps=50)

	gate_momentum_conservation (n=32, steps=200, R=1000.0)

	gate_rho_floor (n=32, steps=200, R=1000.0)

	gate_falling_drop (n=48, D=15, R=800.0, mu_ratio=100.0, steps=500, quiet=False)

	gate_rt (res=(24, 48), R=1000.0, steps=300)

Variables
int	PRESS_MAXIT = 300

int	PRESS_RTOL = 1e-13

dict	SCENES = {"slab": scene_slab, "tilted": scene_tilted, "droplet": scene_droplet}

dict	GATES

	want = sys.argv[1:] or ["uniform_adv", "uniform", "single_phase", "momentum", "floor"]

	t0 = time.time()

Detailed Description

WO-K (rung V2b) — momentum-consistent transport: the gate battery.

The decisive gate is the **uniform-velocity consistency test**: an arbitrary sharp colour field
carried by a spatially uniform velocity, no gravity, no viscosity. A momentum-consistent scheme
holds the velocity uniform to machine precision at ANY density ratio; an inconsistent one is wrong
at O(delta rho), so the test is pass/fail at 1e-15 with no tuning knob — the momentum analogue of
the hydrostatic acid test.

Every gate here also asserts that **no pressure solve hit its iteration cap**. Weymouth-Yue's exact
conservation is conditioned on a discretely divergence-free face field, so an under-solved
projection degrades precisely the quantities these gates measure, and a capped solve can look like
a momentum-consistency failure. A run with a capped solve is reported INVALID, not degraded.

Usage:
    PYTHONPATH=$PWD/build_wok_omp python tests/study/vof_momentum_consistency.py [gate ...]

Function Documentation

◆ all_fluid()

vof_momentum_consistency.all_fluid ( n )

Definition at line 62 of file vof_momentum_consistency.py.

Referenced by gate_falling_drop(), and make_solver().

◆ scene_slab()

vof_momentum_consistency.scene_slab ( n )

Grid-aligned slab: no mixed cell at all (the configuration with the fewest degrees of
freedom, and the one the interface-local CFL band had to be redefined for in WO-J).

Definition at line 69 of file vof_momentum_consistency.py.

◆ scene_tilted()

vof_momentum_consistency.scene_tilted	(	n,
		mx = `0.6`,
		my = `-0.5`,
		mz = `0.62456`
	)

A plane at a generic angle, with exact PLIC fractions from the analytic plane->volume map.

Definition at line 77 of file vof_momentum_consistency.py.

References _plic_volume().

◆ _plic_volume()

vof_momentum_consistency._plic_volume	(	mx,
		my,
		mz,
		alpha
	)

protected

Fluid fraction of the unit cube under mx x + my y + mz z < alpha (independent oracle).

Definition at line 92 of file vof_momentum_consistency.py.

Referenced by scene_tilted().

◆ scene_droplet()

vof_momentum_consistency.scene_droplet	(	n,
		r = `None`
	)

A sphere, sampled by 5-level octree subdivision (exact to ~1e-6 per cell).

Definition at line 136 of file vof_momentum_consistency.py.

References mean().

Referenced by gate_falling_drop(), gate_momentum_conservation(), and gate_rho_floor().

◆ make_solver()

vof_momentum_consistency.make_solver	(	n,
		C,
		rho_g,
		rho_l,
		mu,
		dt,
		U,
		momentum,
		rho0 = `None`
	)

Definition at line 158 of file vof_momentum_consistency.py.

References all_fluid().

Referenced by gate_momentum_conservation(), gate_rho_floor(), gate_single_phase(), gate_uniform(), and gate_uniform_advection_only().

◆ uniform_error()

vof_momentum_consistency.uniform_error	(	s,
		U
	)

Definition at line 175 of file vof_momentum_consistency.py.

Referenced by gate_uniform().

◆ gate_uniform()

vof_momentum_consistency.gate_uniform	(	n = `32`,
		steps = `200`,
		scenes = `("tilted",)`,
		ratios = `(10.0, 1e2, 1e3, 1e4)`
	)

THE gate: uniform velocity at four density ratios, consistent vs inconsistent.

Definition at line 184 of file vof_momentum_consistency.py.

References make_solver(), and uniform_error().

◆ gate_uniform_advection_only()

vof_momentum_consistency.gate_uniform_advection_only	(	n = `32`,
		steps = `1`,
		ratios = `(10.0, 1e2, 1e3, 1e4)`
	)

The same identity on the ADVECTION alone — projection and momentum solve out of the picture.
This isolates whether the two advections truly share fluxes.

Definition at line 212 of file vof_momentum_consistency.py.

References make_solver().

◆ gate_single_phase()

vof_momentum_consistency.gate_single_phase	(	n = `32`,
		steps = `50`
	)

With C == const the consistent advection must be a SINGLE-PHASE transport: bitwise
independent of the density ratio (the rho_g/rho_l factors cancel), and volume-preserving.

Definition at line 238 of file vof_momentum_consistency.py.

References make_solver().

◆ gate_momentum_conservation()

vof_momentum_consistency.gate_momentum_conservation	(	n = `32`,
		steps = `200`,
		R = `1000.0`
	)

Total momentum sum(rho_f u) in a periodic box, no forces: conserved to round-off.

Definition at line 263 of file vof_momentum_consistency.py.

References make_solver(), and scene_droplet().

◆ gate_rho_floor()

vof_momentum_consistency.gate_rho_floor	(	n = `32`,
		steps = `200`,
		R = `1000.0`
	)

The rho^c floor: how often it bites and how much it matters.

Definition at line 297 of file vof_momentum_consistency.py.

References make_solver(), and scene_droplet().

◆ gate_falling_drop()

vof_momentum_consistency.gate_falling_drop	(	n = `48`,
		D = `15`,
		R = `800.0`,
		mu_ratio = `100.0`,
		steps = `500`,
		quiet = `False`
	)

A viscous drop falling under buoyancy at density ratio ~800 and 15 cells/diameter.

WO-K asks for the Arrufat raindrop (ratio 831.8, 15 cells/D, terminal velocity within 15%).
That case is held together by SURFACE TENSION, which is rung V4 — without it a raindrop at its
terminal Weber number flattens and breaks up, so the literal case cannot be run at V2b and a
"terminal velocity" would not exist to measure. The surface-tension-free case with the same
payoff structure is a VISCOUS drop in the Stokes regime, whose terminal velocity is the
Hadamard-Rybczynski result

    U_HR = (2/3) g R^2 (rho_d - rho_c)/mu_c * (mu_c + mu_d)/(2 mu_c + 3 mu_d)

(-> the rigid-sphere Stokes value (2/9) g R^2 drho/mu_c as mu_d/mu_c -> infinity). In a periodic
box the drop feels its own images, so the measured plateau sits below U_HR by the usual
Sangani-Acrivos-type factor at this volume fraction; the number to trust is the CONSISTENT vs
INCONSISTENT comparison at identical settings, with U_HR quoted as the scale.

Buoyancy is imposed as f_z = -(rho - <rho>) g through a LinearMix force closure, so the box
carries no net force and the drop falls relative to a quiescent mean.

Definition at line 320 of file vof_momentum_consistency.py.

References all_fluid(), and scene_droplet().

◆ gate_rt()

vof_momentum_consistency.gate_rt	(	res = `(24, 48)`,
		R = `1000.0`,
		steps = `300`
	)

Rayleigh-Taylor at two resolutions — the WO-K near-Nyquist check (Arrufat section 5).

A momentum-consistent scheme can excite growth near the grid scale on under-resolved shear
layers. Reported here as the interface amplitude growth AND the peak |u| relative to the
inconsistent run at the same resolution; a near-Nyquist artefact shows up as the finer grid
being WORSE, which is the opposite of a convergence signature.

Definition at line 423 of file vof_momentum_consistency.py.

Variable Documentation

◆ PRESS_MAXIT

int vof_momentum_consistency.PRESS_MAXIT = 300

Definition at line 27 of file vof_momentum_consistency.py.

◆ PRESS_RTOL

int vof_momentum_consistency.PRESS_RTOL = 1e-13

Definition at line 28 of file vof_momentum_consistency.py.

◆ SCENES

dict vof_momentum_consistency.SCENES = {"slab": scene_slab, "tilted": scene_tilted, "droplet": scene_droplet}

Definition at line 154 of file vof_momentum_consistency.py.

◆ GATES

dict vof_momentum_consistency.GATES

Initial value:

=  {
    "uniform": gate_uniform,
    "uniform_adv": gate_uniform_advection_only,
    "single_phase": gate_single_phase,
    "momentum": gate_momentum_conservation,
    "floor": gate_rho_floor,
    "drop": gate_falling_drop,
    "rt": gate_rt,
}

Definition at line 498 of file vof_momentum_consistency.py.

◆ want

vof_momentum_consistency.want = sys.argv[1:] or ["uniform_adv", "uniform", "single_phase", "momentum", "floor"]

Definition at line 509 of file vof_momentum_consistency.py.

◆ t0

vof_momentum_consistency.t0 = time.time()

Definition at line 511 of file vof_momentum_consistency.py.

Classes

Functions

Variables