packing2d Namespace Reference

Classes
class	Cell
class	System

Functions
	sdf (p, R)
	center_of (p)
	k_PH (G, kf, ks)
	bilin (G, ids_fn, p, valid)
	k_P2F (G, kf, ks, gapaware=False, c=0.7)

Variables
	C0 = np.array([0.5, 0.5])
list	IMG = [np.array([a, b], float) for a in (-1, 0, 1) for b in (-1, 0, 1)]
int	ks = float(sys.argv[1]) if len(sys.argv) > 1 else 100.0
list	gaps = [float(a) for a in sys.argv[2:]] or [0.2, 0.05, 0.02]
float	R = 0.5 * (1 - gap)
dict	res = {}
	G = Cell(n, R, off=(0.0, 0.0))
	q
	st
	gapaware
	flush
dict	v = v[-1] + (v[-1] - v[-2]) / 3

Detailed Description

2-D prototype, round 8: NEAR-CONTACT conjugate conduction.

Effective conductivity of a periodic square array of cylinders (unit cell, cylinder radius R at the
centre), macroscopic gradient dT/dx = -1, k_f = 1.  Gap g = 1 - 2R from 0.2 down to 0.01.
Unknowns are periodic: T(x) = theta - x.  k_eff = total +x heat flux through a face column.

Methods
  P2F    two-field probe-flux cut-cell FV (conj.py), probe 0.7h, round-4 fallback ladder
         (renormalised valid weights -> 1.0h -> 1.5h).  A probe landing inside ANOTHER solid image
         is not detected (the current design's blind spot).
  P2Fg   P2F + gap-aware fluid probe: s_f = min(0.7h, 0.5 * normal distance to the next solid)
  PH     Peters' hybrid (his 3-D packing code construct_flux_ibm.m, transcribed to 2-D):
           simple crossing face (1 crossing, 2 same-phase cells each side) -> directional
             min-curvature quadratic, aperture-weighted branches;
           close / very close crossing face -> appendix series-parallel
             k_eff = [k_f + (k_s-k_f) a_s (1-n_x^2)] / [1 + (k_f/k_s - 1) l_s n_x^2]
             (l_s = solid fraction of the centre line);
           cut non-crossing face -> k_f + (k_s-k_f) a_s (1-n_x^2) (fluid centres; mirror for solid).
Reference: Richardson extrapolation (p = 2) of the two finest resolutions, compared across methods.

Function Documentation

sdf()

packing2d.sdf	(		p,
			R
	)

Definition at line 28 of file packing2d.py.

Referenced by k_P2F(), and k_PH().

center_of()

packing2d.center_of

(

p

)

Definition at line 32 of file packing2d.py.

Referenced by k_P2F(), and k_PH().

k_PH()

packing2d.k_PH	(		G,
			kf,
			ks
	)

Definition at line 80 of file packing2d.py.

References center_of(), and sdf().

bilin()

packing2d.bilin	(		G,
			ids_fn,
			p,
			valid
	)

Definition at line 129 of file packing2d.py.

Referenced by k_P2F().

k_P2F()

packing2d.k_P2F	(		G,
			kf,
			ks,
			gapaware = False,
			c = 0.7
	)

Definition at line 141 of file packing2d.py.

References bilin(), center_of(), and sdf().

Variable Documentation

C0

packing2d.C0 = np.array([0.5, 0.5])

Definition at line 24 of file packing2d.py.

IMG

list packing2d.IMG = [np.array([a, b], float) for a in (-1, 0, 1) for b in (-1, 0, 1)]

Definition at line 25 of file packing2d.py.

ks

packing2d.ks = float(sys.argv[1]) if len(sys.argv) > 1 else 100.0

Definition at line 212 of file packing2d.py.

gaps

list packing2d.gaps = [float(a) for a in sys.argv[2:]] or [0.2, 0.05, 0.02]

Definition at line 213 of file packing2d.py.

R

float packing2d.R = 0.5 * (1 - gap)

Definition at line 215 of file packing2d.py.

res

dict packing2d.res = {}

Definition at line 216 of file packing2d.py.

G

packing2d.G = Cell(n, R, off=(0.0, 0.0))

Definition at line 218 of file packing2d.py.

q

packing2d.q

Definition at line 220 of file packing2d.py.

st

packing2d.st

Definition at line 220 of file packing2d.py.

gapaware

packing2d.gapaware

Definition at line 221 of file packing2d.py.

flush

packing2d.flush

Definition at line 223 of file packing2d.py.

v

dict packing2d.v = v[-1] + (v[-1] - v[-2]) / 3

Definition at line 225 of file packing2d.py.