Functions
	ux (x, y, z)

	sdf (x, y, z)

	reference (M=200000, d=1e-6)

	face_openness (N, axis, h)

	run (N, use_far2=False)

	_quad (x, a1, a2, a3)

	run_normal (N, analytic=False)

Variables
float	R = 0.3102

	C0 = np.array([0.013, -0.007, 0.004])

float	MU = 0.1

	Fex = reference()

	pA = None

	r = run(N)

int	eA = 100*(r["FB"]-Fex)/abs(Fex)

int	eC = 100*(r["Fcen"]-Fex)/abs(Fex)

	oA = np.log2(abs(pA)/abs(eA)) if pA else float("nan")

	oB = np.log2(abs(pB)/abs(eB)) if pB else float("nan")

float	fac = np.log2(N/pN) if pA else 1.0

	pB

	pN

	pC = None

	oC = np.log2(abs(pC) / abs(eC)) / np.log2(N / pN2) if pC else float("nan")

	pN2

Detailed Description

A-priori test of the fully-FV cut-cell wall viscous flux with 7-point ingredients.

Estimator (what the proposed FV collocated momentum assembly would compute):
  F_est = mu * sum_cells sum_a W_a * g_a
  - W_a = h^2 (o_{a-} - o_{a+}) : the wall fragment's area-weighted fluid-outward normal,
          FREE from the face openness by the divergence theorem (no surface reconstruction).
  - g_a : d(ux)/da at the wall from the UNIDIRECTIONAL wall-anchored quadratic along axis a
          through {u(wall)=0, U_c, U_far} -- strictly 7-point data. Central difference where
          the axis does not cross the wall; solid-center cells borrow the adjacent fluid
          cell's gradient vector.
Reference: F_exact = mu * closed-surface integral of grad(ux).n dA (n = fluid-outward = -rhat),
by Fibonacci quadrature of the analytic Stokes solution. Note grad(ux) = n * d(ux)/dn EXACTLY
on the wall (no-slip kills tangential derivatives), so the axis decomposition misses nothing
structurally; the test measures fit truncation + evaluation-point displacement + attribution.
Face openness computed semi-analytically (256-point chord integration of the exact disk cut),
so the fragment identity is near-exact and the GRADIENT estimator is what is being tested.

Function Documentation

◆ ux()

fv_wallflux_apriori.ux	(	x,
		y,
		z
	)

Definition at line 24 of file fv_wallflux_apriori.py.

Referenced by reference(), run(), and run_normal().

◆ sdf()

fv_wallflux_apriori.sdf	(	x,
		y,
		z
	)

Definition at line 29 of file fv_wallflux_apriori.py.

Referenced by run(), and run_normal().

◆ reference()

fv_wallflux_apriori.reference	(	M = `200000`,
		d = `1e-6`
	)

Definition at line 32 of file fv_wallflux_apriori.py.

References ux().

◆ face_openness()

fv_wallflux_apriori.face_openness	(	N,
		axis,
		h
	)

Fluid area fraction of every face perpendicular to `axis`, shape (N+1,N,N) in
(plane, t1, t2) order; t1,t2 = the other two axes in cyclic order. Semi-analytic:
the sphere cuts the face plane in a disk; per cut face integrate the chord (256 pts).

Definition at line 42 of file fv_wallflux_apriori.py.

Referenced by run(), and run_normal().