flatwall_displacement Namespace Reference

Functions
	channel (N, s)
	exact_profile (exp, y, w_lo, w_hi)
	exact_discharge (exp, w_lo, w_hi)
	make_solver (kind, N, s)
	set_forces (sol, exp, ny, w_lo, w_hi)
	march (sol)
	run (kind, exp, N, s)

Variables
	MU
	F0
int	NX = 8
int	SLAB = 8
	TOL = float(os.environ.get("MARCH_TOL", "1e-9"))
	CAP = int(os.environ.get("MARCH_MAX", "8000"))
	DT = float(os.environ.get("DT", "60.0"))
	ap = argparse.ArgumentParser()
	default
	a = ap.parse_args()
list	Ns = [int(x) for x in a.N.split(",")]
list	Ss = [float(x) for x in a.s.split(",")]
	exps = a.exp.split(",")
	kinds = a.solvers.split(",")
str	hdr = f"{'N':>4} {'s':>5} {'solver':>12} {'steps':>6} {'e_flux':>11} {'e_cell':>11} {'L2prof':>10}"
	flush
dict	base = {}
	r = run(kind, exp, N, s)
tuple	row
dict	r1 = base.get(kind)
	du = float(np.abs(r['U'] - r1['U']).max()) / r['uscale']
	dv = float(np.abs(r['V']).max()) / r['uscale']

Detailed Description

Flat-wall displacement sweep (Frank's isolation ladder, 2026-08-20): the collocated ceiling
hunted in the simplest IBM geometry -- a plane channel whose walls sit at a FRACTIONAL grid offset
s, so every cut cell has the same theta and the closure error is a coherent function of one
parameter instead of an average over random incidences.

Steady-state structure (doc/collocated_accuracy_ceiling.md + the joint-fixed-point argument): the
collocated steady state satisfies  nu*L_ibm(u) + F = G_gp(P)  with  D_alpha(avg_half(u)) = 0.
In a wall-aligned channel these decouple, giving three isolating experiments:

  E1   uniform Fx           -> parabola.  u = u(y) x-only => div == 0 discretely, P == 0: the
                               pressure machinery NEVER ENGAGES.  Any error is the momentum IBM
                               closure L_ibm alone (suspect S4).  (Caveat: 2nd-order closures can
                               be exact on parabolas -- a null here does not clear curved walls.)
  E1b  Fx(y)=F0 cos(k(y-yc)), k=pi/W -> u = F0/(mu k^2) cos(k(y-yc)), zero at both walls,
                               non-polynomial: the order of L_ibm is readable.
  E2   E1's Fx  PLUS  Fy(y)=A sin(2pi(y-w_lo)/W) in the fluid -> exact answer: u IDENTICAL to E1,
                               v == 0, p = integral(Fy).  The y-force must be absorbed ENTIRELY by
                               the discrete pressure.  Any (u - u_E1, v != 0) response is a defect
                               of the (G_gp vs masked-half-average constraint) pair -- the
                               non-adjointness channel, with L_ibm differenced out.

Sweep s in [0,1) x N (channel width in cells) x solver in {stag, gauge-exact (mode 9), plain
(mode 0)}.  Errors are reported on the conserved face flux (primary; mean(alpha_x*uf)) and the
cell mean, both relative to the exact discharge.

  SDFLOW_BUILD=build_omp3 python tests/study/flatwall_displacement.py            # default sweep
  ... flatwall_displacement.py --N 8,16,32,64 --s 0.1,0.3,0.5,0.7,0.9 --exp E1,E1b,E2

Function Documentation

channel()

flatwall_displacement.channel	(		N,
			s
	)

SDF (F-order (nx,ny,nz)) + wall positions for a width-N channel displaced by s cells.

Definition at line 48 of file flatwall_displacement.py.

Referenced by make_solver().

exact_profile()

flatwall_displacement.exact_profile	(		exp,
			y,
			w_lo,
			w_hi
	)

Definition at line 59 of file flatwall_displacement.py.

Referenced by run().

exact_discharge()

flatwall_displacement.exact_discharge	(		exp,
			w_lo,
			w_hi
	)

Definition at line 70 of file flatwall_displacement.py.

Referenced by run().

make_solver()

flatwall_displacement.make_solver	(		kind,
			N,
			s
	)

Definition at line 78 of file flatwall_displacement.py.

References channel().

Referenced by run().

set_forces()

flatwall_displacement.set_forces	(		sol,
			exp,
			ny,
			w_lo,
			w_hi
	)

Definition at line 96 of file flatwall_displacement.py.

Referenced by run().

march()

flatwall_displacement.march

(

sol

)

Definition at line 120 of file flatwall_displacement.py.

Referenced by run().

run()

flatwall_displacement.run	(		kind,
			exp,
			N,
			s
	)

Definition at line 132 of file flatwall_displacement.py.

References exact_discharge(), exact_profile(), make_solver(), march(), and set_forces().

Variable Documentation

MU

flatwall_displacement.MU

Definition at line 40 of file flatwall_displacement.py.

F0

flatwall_displacement.F0

Definition at line 40 of file flatwall_displacement.py.

NX

int flatwall_displacement.NX = 8

Definition at line 41 of file flatwall_displacement.py.

SLAB

int flatwall_displacement.SLAB = 8

Definition at line 42 of file flatwall_displacement.py.

TOL

flatwall_displacement.TOL = float(os.environ.get("MARCH_TOL", "1e-9"))

Definition at line 43 of file flatwall_displacement.py.

CAP

flatwall_displacement.CAP = int(os.environ.get("MARCH_MAX", "8000"))

Definition at line 44 of file flatwall_displacement.py.

DT

flatwall_displacement.DT = float(os.environ.get("DT", "60.0"))

Definition at line 45 of file flatwall_displacement.py.

ap

flatwall_displacement.ap = argparse.ArgumentParser()

Definition at line 155 of file flatwall_displacement.py.

default

flatwall_displacement.default

Definition at line 156 of file flatwall_displacement.py.

a

flatwall_displacement.a = ap.parse_args()

Definition at line 160 of file flatwall_displacement.py.

Ns

list flatwall_displacement.Ns = [int(x) for x in a.N.split(",")]

Definition at line 161 of file flatwall_displacement.py.

Ss

list flatwall_displacement.Ss = [float(x) for x in a.s.split(",")]

Definition at line 162 of file flatwall_displacement.py.

exps

flatwall_displacement.exps = a.exp.split(",")

Definition at line 163 of file flatwall_displacement.py.

kinds

flatwall_displacement.kinds = a.solvers.split(",")

Definition at line 164 of file flatwall_displacement.py.

hdr

flatwall_displacement.hdr = f"{'N':>4} {'s':>5} {'solver':>12} {'steps':>6} {'e_flux':>11} {'e_cell':>11} {'L2prof':>10}"

Definition at line 167 of file flatwall_displacement.py.

flush

flatwall_displacement.flush

Definition at line 170 of file flatwall_displacement.py.

base

dict flatwall_displacement.base = {}

Definition at line 173 of file flatwall_displacement.py.

r

flatwall_displacement.r = run(kind, exp, N, s)

Definition at line 175 of file flatwall_displacement.py.

row

flatwall_displacement.row

Initial value:

=  (f"{N:>4} {s:>5.2f} {kind:>12} {r['steps']:>6} "
                           f"{r['e_flux']:>+11.3e} {r['e_cell']:>+11.3e} {r['l2']:>10.3e}")

Definition at line 176 of file flatwall_displacement.py.

r1

flatwall_displacement.r1 = base.get(kind)

Definition at line 180 of file flatwall_displacement.py.

du

flatwall_displacement.du = float(np.abs(r['U'] - r1['U']).max()) / r['uscale']

Definition at line 183 of file flatwall_displacement.py.

dv

flatwall_displacement.dv = float(np.abs(r['V']).max()) / r['uscale']

Definition at line 184 of file flatwall_displacement.py.