rayleigh_taylor Namespace Reference

Functions
	hydrostatic (ratio, mu=0.0, steps=100, g=0.1, dt=1.0, N=8, NZ=24)
	rayleigh_taylor (N=48, NZ=96, g=0.005, mu=0.002, dt=1.0, steps=240)
	rayleigh_taylor_vof (N=48, NZ=96, g=0.005, mu=0.002, steps=240, cfl=0.2, dt0=1.0)
	fit (a, t, t0=40.0, t1=160.0)

Variables
	m
	perr
	hist = rayleigh_taylor()
	growth = hist[-1] / hist[0]
	vh
	vt
	vdrift
	vgrowth = vh[-1] / vh[0]
	A
	k
	n_lin = np.sqrt(A * 0.005 * k)
list	td = [40.0 * i for i in range(len(hist))]
	n_dif
	n_vof

Detailed Description

Variable-density validation (Phase 5): hydrostatic acid tests + Rayleigh-Taylor demonstrator.

1. Hydrostatic balance (the acid test): a stratified two-layer fluid at rest under gravity must
   STAY at rest, with the discrete pressure gradient exactly rho_face*g. This detects any
   inconsistency between the momentum face density, the body-force face value, and the projection
   face coefficient. Inviscid: max steady velocity ~1e-16, P-gradient error ~1e-16 at density
   ratios 3 AND 1000. (The C++ ctest `vardensity_projection` runs the same case.)

2. Rayleigh-Taylor: heavy over light (ratio 3, Atwood 0.5) through the FULL two-phase chain — a
   TRANSPORTED phase fraction c drives rho via a linear-mixture closure (auto-enabling the
   variable-density path), gravity is a closure force_z = -g*rho, momentum + projection carry the
   variable density. The interface amplitude grows ~exponentially then nonlinearly; the measured
   growth rate is ~0.75x the inviscid sqrt(A g k) (viscous + finite-interface damping).

   TWO records, same physics, reported side by side (VoF rung V2a / WO-J):
     * DIFFUSE C — the pre-VoF baseline: a tanh profile of width 1.5 advected by the Koren TVD
       scalar transport. Amplitude 1.50 -> 19.52 (x13.0), rate 0.75x sqrt(A g k).
     * SHARP C — geometric VoF (PLIC + Weymouth-Yue), adaptive dt from the INTERFACE-LOCAL
       Courant number. Amplitude 1.50 -> 20.20 (x13.5), rate 0.77x sqrt(A g k), colour volume
       drift -6.6e-09. The sharp interface grows marginally FASTER, which is the expected sign:
       a two-cell-wide density ramp damps the mode that a sharp jump does not.

Run:  PYTHONPATH=<build> python rayleigh_taylor.py

Function Documentation

hydrostatic()

rayleigh_taylor.hydrostatic	(		ratio,
			mu = 0.0,
			steps = 100,
			g = 0.1,
			dt = 1.0,
			N = 8,
			NZ = 24
	)

Definition at line 30 of file rayleigh_taylor.py.

rayleigh_taylor()

rayleigh_taylor.rayleigh_taylor	(		N = 48,
			NZ = 96,
			g = 0.005,
			mu = 0.002,
			dt = 1.0,
			steps = 240
	)

Definition at line 52 of file rayleigh_taylor.py.

rayleigh_taylor_vof()

rayleigh_taylor.rayleigh_taylor_vof	(		N = 48,
			NZ = 96,
			g = 0.005,
			mu = 0.002,
			steps = 240,
			cfl = 0.2,
			dt0 = 1.0
	)

SHARP-interface Rayleigh-Taylor through the geometric VoF chain (rung V2a, WO-J).

Identical physics to `rayleigh_taylor()` above — same grid, same Atwood number (ratio 3),
same gravity, same viscosity, same initial interface z_i(x) = NZ/2 + 1.5 cos(2 pi x / N) —
with ONE difference: the phase field is a sharp geometric VoF colour field advected by
Weymouth-Yue instead of a tanh profile of width 1.5 advected by Koren TVD. Reporting both is
the point: the diffuse record is the pre-VoF baseline this rung has to reproduce.

Two deliberate departures from the diffuse driver, both forced by the method rather than
chosen:

* dt is ADAPTIVE. Weymouth-Yue is bounded only for an interface-local Courant number below
  1/(2(N-1)) = 0.25 in 3D, and an RT interface accelerates, so a fixed dt = 1 that is safe at
  t = 0 is not safe at t = 240. dt is therefore chosen from `vof_max_courant()` — the
  INTERFACE-LOCAL Courant number, which is the quantity the bound applies to (a global max
  would throttle on the far-field return flow; V1 measured 2x over-throttling on Zalesak, and
  the WO-J ctest measures 22x on a jet-plus-quiescent-interface scene). Amplitudes are
  therefore reported against PHYSICAL TIME, sampled at the same t = 40, 80, ... 240 as the
  diffuse record.

* the amplitude comes from the COLUMN SUM of C, not from interpolating a C = 0.5 crossing.
  For a sharp interface the column sum IS the interface height to machine precision
  (z_i = NZ - sum_z C, heavy on top), while a 0.5-crossing interpolation of a two-cell-wide
  profile carries an O(h) bias that the diffuse case cannot avoid and this one need not.

Definition at line 82 of file rayleigh_taylor.py.

fit()

rayleigh_taylor.fit	(		a,
			t,
			t0 = 40.0,
			t1 = 160.0
	)

Definition at line 166 of file rayleigh_taylor.py.

Variable Documentation

m

rayleigh_taylor.m

Definition at line 144 of file rayleigh_taylor.py.

perr

rayleigh_taylor.perr

Definition at line 144 of file rayleigh_taylor.py.

hist

rayleigh_taylor.hist = rayleigh_taylor()

Definition at line 147 of file rayleigh_taylor.py.

growth

rayleigh_taylor.growth = hist[-1] / hist[0]

Definition at line 148 of file rayleigh_taylor.py.

vh

rayleigh_taylor.vh

Definition at line 153 of file rayleigh_taylor.py.

vt

rayleigh_taylor.vt

Definition at line 153 of file rayleigh_taylor.py.

vdrift

rayleigh_taylor.vdrift

Definition at line 153 of file rayleigh_taylor.py.

vgrowth

rayleigh_taylor.vgrowth = vh[-1] / vh[0]

Definition at line 154 of file rayleigh_taylor.py.

A

rayleigh_taylor.A

Definition at line 163 of file rayleigh_taylor.py.

k

rayleigh_taylor.k

Definition at line 163 of file rayleigh_taylor.py.

n_lin

rayleigh_taylor.n_lin = np.sqrt(A * 0.005 * k)

Definition at line 164 of file rayleigh_taylor.py.

td

list rayleigh_taylor.td = [40.0 * i for i in range(len(hist))]

Definition at line 170 of file rayleigh_taylor.py.

n_dif

rayleigh_taylor.n_dif

Definition at line 171 of file rayleigh_taylor.py.

n_vof

rayleigh_taylor.n_vof

Definition at line 171 of file rayleigh_taylor.py.