Functions
	_grid (N)

	_mm (d, N)

	sdf_zh (N, phi=0.216)

	sdf_random (N, n=8, r_frac=0.18, jit=0.06, seed=12345)

	run (case, N, solver="staggered", re=0.0, mu=0.1, F=1e-3, dt=60.0, max_steps=500, tol=1e-6)

Variables
list	ZH_PHI = [0.000125,0.001,0.008,0.027,0.064,0.125,0.216,0.343,0.45,0.5236]

list	ZH_K = [1.096,1.212,1.525,2.008,2.810,4.292,7.442,15.4,28.1,42.1]

float	zh_ref = lambda phi(np.interp(phi, ZH_PHI, ZH_K))

list	cases = [("zh",[16,24,32,48]), ("random",[24,32,48])]

	flush

float	ref = "zh" else None

	r = run(case,N,solver,re=0.0); gc.collect()

str	err = f"{100*(r['val']-ref)/ref:+.2f}%" if ref else ""

Detailed Description

sdflow side of the three-solver study: staggered vs collocated, Z&H SC sphere + random packing,
Re=0 (Stokes) and Re=100 (advection on). Prints K (Z&H) / k* (random), cells, pressure iters, wall.
Geometry + metrics identical to tests/regression/sdflow_regression.py so AMR can be compared directly.
Pair with transport-core/python/amr_drag_study.py for the AMR (graded cut-cell) side.

Findings (2026-06-25):
  * Z&H phi=0.216 (ref K=7.442), Re=0: staggered converges 2nd-order from below
    (N=16 -1.78% -> N=48 -0.07%); collocated carries the intrinsic +~1% gap (N=32 +1.16%).
  * random pack k*: staggered -> ~0.00622 from above, collocated -> ~0.00618 from below (same k_inf).
  * Re~100 (F=2.6e-3, N=32): staggered K=8.90 (Re=101.6), collocated K=9.05 (Re=99.9), ~+20% over
    Stokes; both converge cleanly (div~1e-12). Same F at N=48 gives Re~300 (R scales with N) -- only
    N=32 is a true Re=100 comparison.
  * Staggered is the accuracy default for permeability/drag; collocated trades ~1%/grid for
    cell-centered storage. (Kokkos/OpenMP: ~1-30 s per case.)

Function Documentation

◆ _grid()

three_solver_study._grid ( N )

protected

Definition at line 25 of file three_solver_study.py.

Referenced by sdf_random(), and sdf_zh().

◆ _mm()

three_solver_study._mm	(	d,
		N
	)

protected

Definition at line 27 of file three_solver_study.py.

Referenced by sdf_random().

◆ sdf_zh()

three_solver_study.sdf_zh	(	N,
		phi = `0.216`
	)

Definition at line 29 of file three_solver_study.py.

References _grid().

Referenced by run().

◆ sdf_random()

three_solver_study.sdf_random	(	N,
		n = `8`,
		r_frac = `0.18`,
		jit = `0.06`,
		seed = `12345`
	)

Definition at line 33 of file three_solver_study.py.

References _grid(), and _mm().

Referenced by run().

◆ run()

three_solver_study.run	(	case,
		N,
		solver = `"staggered"`,
		re = `0.0`,
		mu = `0.1`,
		F = `1e-3`,
		dt = `60.0`,
		max_steps = `500`,
		tol = `1e-6`
	)

Definition at line 42 of file three_solver_study.py.

References sdf_random(), and sdf_zh().

Variable Documentation

◆ ZH_PHI

list three_solver_study.ZH_PHI = [0.000125,0.001,0.008,0.027,0.064,0.125,0.216,0.343,0.45,0.5236]

Definition at line 21 of file three_solver_study.py.

◆ ZH_K

list three_solver_study.ZH_K = [1.096,1.212,1.525,2.008,2.810,4.292,7.442,15.4,28.1,42.1]

Definition at line 22 of file three_solver_study.py.

◆ zh_ref

float three_solver_study.zh_ref = lambda phi(np.interp(phi, ZH_PHI, ZH_K))

Definition at line 23 of file three_solver_study.py.

◆ cases

list three_solver_study.cases = [("zh",[16,24,32,48]), ("random",[24,32,48])]

Definition at line 72 of file three_solver_study.py.

◆ flush

three_solver_study.flush

Definition at line 73 of file three_solver_study.py.

◆ ref

float three_solver_study.ref = "zh" else None

Definition at line 75 of file three_solver_study.py.

◆ r

three_solver_study.r = run(case,N,solver,re=0.0); gc.collect()

Definition at line 79 of file three_solver_study.py.

◆ err

str three_solver_study.err = f"{100*(r['val']-ref)/ref:+.2f}%" if ref else ""

Definition at line 80 of file three_solver_study.py.

Functions

Variables