rotlet_gate Namespace Reference

Functions
	rotlet (px, py, pz, R, w)
	rotlet_lattice (px, py, pz, R, w, L, nimg)
	run (N, crossings=False)
	err (res, shell, nimg=None)
	order_study ()
	reference_probe ()

Variables
	RF = float(os.environ.get("ROTLET_RF", "0.10"))
float	OMEGA = 0.02
	MU
	RHO
	DT
	STEPS
tuple	NEAR = (1.15, 2.0)
tuple	FAR = (2.0, 3.5)
	KN_R
	KI_I
	KI_R
tuple	OFFS = ((-0.5, 0.0, 0.0), (0.0, -0.5, 0.0), (0.0, 0.0, -0.5))

Detailed Description

Layer 3 rungs 2-3 gate: ROTLET. A single sphere spinning in Stokes flow.

Exact exterior solution for a sphere of radius R spinning at omega in UNBOUNDED Stokes flow:
    u(r) = (R/|r|)^3 * (omega x r)
a pure rotational (couplet) field: zero net force, decaying as 1/|r|^2.

The solver's box is PERIODIC, so the true solution is the lattice of images, not the unbounded
rotlet. That difference is physics, not discretisation error, and it does not shrink under
refinement -- so the error is measured against BOTH references and the lattice sum's own
convergence (9^3 vs 13^3 images) is printed, so a reader can see whether the reference is
trustworthy before trusting an order taken against it.

SAMPLING. get_u/get_v/get_w return MAC FACE values -- u at (i-1/2,j,k), v at (i,j-1/2,k), w at
(i,j,k-1/2). Comparing them against the analytic field sampled at CELL CENTRES injects an O(h)
offset that caps the measured order at 1 however accurate the solver is. Each component is
therefore compared at its own staggered point.

Two shells: the near band [1.15R, 2R], a few cells off a curved cut wall, and a far band
[2R, 3.5R]. Order is the claim, not the absolute.

Function Documentation

rotlet()

rotlet_gate.rotlet	(		px,
			py,
			pz,
			R,
			w
	)

Unbounded rotlet, omega = (0,0,w).

Definition at line 34 of file rotlet_gate.py.

Referenced by err(), and rotlet_lattice().

rotlet_lattice()

rotlet_gate.rotlet_lattice	(		px,
			py,
			pz,
			R,
			w,
			L,
			nimg
	)

Rotlet summed over a (2*nimg+1)^3 block of periodic images.

Definition at line 41 of file rotlet_gate.py.

References rotlet().

Referenced by err().

run()

rotlet_gate.run	(		N,
			crossings = False
	)

Definition at line 52 of file rotlet_gate.py.

Referenced by order_study(), and reference_probe().

err()

rotlet_gate.err	(		res,
			shell,
			nimg = None
	)

Relative L2 error over `shell`; lattice reference when nimg is given, unbounded otherwise.

Definition at line 89 of file rotlet_gate.py.

References rotlet(), and rotlet_lattice().

Referenced by order_study(), and reference_probe().

order_study()

rotlet_gate.order_study

(

)

Definition at line 114 of file rotlet_gate.py.

References err(), and run().

Referenced by reference_probe().

reference_probe()

rotlet_gate.reference_probe

(

)

IS THE PLATEAU THE SOLVER OR THE REFERENCE?

Decisive experiment: hold R fixed IN CELLS (so the discretisation error is unchanged) and
change only the box, i.e. only R/L. The naive periodic-image correction to an unbounded rotlet
scales like (r/L)^3 at fixed r/R, so halving R/L must drop it ~8x; the discretisation error
cannot move at all. Whatever the near-shell error does is therefore attributable.

Definition at line 140 of file rotlet_gate.py.

References err(), order_study(), reference_probe(), and run().

Referenced by reference_probe().

Variable Documentation

RF

rotlet_gate.RF = float(os.environ.get("ROTLET_RF", "0.10"))

Definition at line 26 of file rotlet_gate.py.

OMEGA

float rotlet_gate.OMEGA = 0.02

Definition at line 27 of file rotlet_gate.py.

MU

rotlet_gate.MU

Definition at line 28 of file rotlet_gate.py.

RHO

rotlet_gate.RHO

Definition at line 28 of file rotlet_gate.py.

DT

rotlet_gate.DT

Definition at line 28 of file rotlet_gate.py.

STEPS

rotlet_gate.STEPS

Definition at line 28 of file rotlet_gate.py.

NEAR

tuple rotlet_gate.NEAR = (1.15, 2.0)

Definition at line 29 of file rotlet_gate.py.

FAR

tuple rotlet_gate.FAR = (2.0, 3.5)

Definition at line 30 of file rotlet_gate.py.

KN_R

rotlet_gate.KN_R

Definition at line 31 of file rotlet_gate.py.

KI_I

rotlet_gate.KI_I

Definition at line 31 of file rotlet_gate.py.

KI_R

rotlet_gate.KI_R

Definition at line 31 of file rotlet_gate.py.

OFFS

tuple rotlet_gate.OFFS = ((-0.5, 0.0, 0.0), (0.0, -0.5, 0.0), (0.0, 0.0, -0.5))

Definition at line 86 of file rotlet_gate.py.