conj_peters Namespace Reference

Classes
class	Box

Functions
	exact (x, y, k1, k2)
	lagr_d (nodes, x, order)
	dir_face (xi)
	dir_face_both (xi)
	dir_face_flux (xi, kl, kr)
	dir_face_closed (xi)
	crossing (G, P, Q, axis)
	solve_one_field (G, k1, k2, method)
	norms (G, T, k1, k2)
	solve_p2f (G, k1, k2, c=0.7)

Variables
float	R = 1.0
float	L = 5.0
	atol
	methods = sys.argv[1:] or ["OF-h", "OF-a", "GFM", "DIR", "DIR-B"]
	rng = rng.random((2, 2))
list	NDs = [16, 32, 64, 128]
str	line = 0
list	ee = []
	G = Box(ND, o)
	T
	nfb
list	prev = ee[0]
	flush

Detailed Description

2-D prototype, round 7: Frank Peters' directional conjugate IBM (~/Codes/conjugate/
IBM_conjugated_transport.tex) against the other conjugate candidates, on HIS test problem.

Test (tex sec. Results): steady -div(k grad T) = 0, disc r < R = 1 with k2, k1 = 1 outside, in a
square of side 5 with Dirichlet values from the exact infinite-domain solution
    inside : T = 2 k1/(k1+k2) x ;   outside: T = x + (k1-k2)/(k1+k2) R^2 x / r^2.
Errors at cell centres (L1, L2, Linf as in the tex), k2 = 0.01, 0.5, 2, 100.

Methods (all finite-volume on cell-centred unknowns; one cell = the phase of its centre unless noted)
  OF-h   one field, harmonic mean of the two cell conductivities on a face ("one field")
  OF-a   one field, face conductivity = aperture-weighted arithmetic mean a k1 + (1-a) k2
  GFM    one field, series coefficient across the crossing (Liu-Fedkiw-Kang 2000):
         k_f = 1/((1/2+xi)/k_P + (1/2-xi)/k_Q) on faces whose centre line crosses the interface
  DIR    Peters' directional scheme: on a crossing line, quadratics through (-3/2, -1/2, xi) and
         (xi, 1/2, 3/2) sharing T_xi; T_xi minimises T''(xi-)^2 + T''(xi+)^2 (eq. 12); the face
         flux is k(side of x=0) T'(0) (eq. 13/14). Non-crossing faces use the phase k.
         Fallback (no second same-phase cell on a side): GFM coefficient.
  DIR-B  DIR + the appendix "second approach" effective conductivity on faces that are CUT but whose
         centre line does not cross (k_eff with a_s, l_s = 0, n_x).
  P2F    two-field probe-flux cut-cell FV (conj.py): fluid and solid unknowns in cut cells, probe
         0.7h each side, 2x2 elimination per facet (error read from the DOF of the centre's phase).

Function Documentation

exact()

conj_peters.exact	(		x,
			y,
			k1,
			k2
	)

Definition at line 29 of file conj_peters.py.

Referenced by norms(), solve_one_field(), and solve_p2f().

lagr_d()

conj_peters.lagr_d	(		nodes,
			x,
			order
	)

weights w with p^(order)(x) = sum w_j f_j for the Lagrange polynomial through nodes.

Definition at line 50 of file conj_peters.py.

Referenced by dir_face(), dir_face_both(), and dir_face_flux().

dir_face()

conj_peters.dir_face

(

xi

)

Peters' face derivative T'(0) = sum w_j T_j over (T_-3/2, T_-1/2, T_1/2, T_3/2), unit spacing.

Definition at line 62 of file conj_peters.py.

References lagr_d().

Referenced by solve_one_field().

dir_face_both()

conj_peters.dir_face_both

(

xi

)

(left-branch row, right-branch row) of T'(0) over (T-3/2, T-1/2, T1/2, T3/2), shared min-curvature T_xi.

Definition at line 76 of file conj_peters.py.

References lagr_d().

dir_face_flux()

conj_peters.dir_face_flux	(		xi,
			kl,
			kr
	)

as dir_face_both, but T_xi from FLUX continuity kl T'_l(xi) = kr T'_r(xi) (k-aware).

Definition at line 87 of file conj_peters.py.

References lagr_d().

Referenced by solve_one_field().

dir_face_closed()

conj_peters.dir_face_closed

(

xi

)

the tex's closed form (eq. after 'with f_A ...'), to cross-check dir_face.

Definition at line 99 of file conj_peters.py.

crossing()

conj_peters.crossing	(		G,
			P,
			Q,
			axis
	)

xi in (-1/2, 1/2): crossing of the segment P->Q (unit spacing, face at 0) with the circle.

Definition at line 109 of file conj_peters.py.

Referenced by solve_one_field().

solve_one_field()

conj_peters.solve_one_field	(		G,
			k1,
			k2,
			method
	)

Definition at line 118 of file conj_peters.py.

References crossing(), dir_face(), dir_face_flux(), and exact().

norms()

conj_peters.norms	(		G,
			T,
			k1,
			k2
	)

Definition at line 209 of file conj_peters.py.

References exact().

solve_p2f()

conj_peters.solve_p2f	(		G,
			k1,
			k2,
			c = 0.7
	)

Definition at line 217 of file conj_peters.py.

References exact().

Variable Documentation

R

float conj_peters.R = 1.0

Definition at line 25 of file conj_peters.py.

L

float conj_peters.L = 5.0

Definition at line 26 of file conj_peters.py.

atol

conj_peters.atol

Definition at line 276 of file conj_peters.py.

methods

list conj_peters.methods = sys.argv[1:] or ["OF-h", "OF-a", "GFM", "DIR", "DIR-B"]

Definition at line 278 of file conj_peters.py.

rng

conj_peters.rng = rng.random((2, 2))

Definition at line 279 of file conj_peters.py.

NDs

list conj_peters.NDs = [16, 32, 64, 128]

Definition at line 282 of file conj_peters.py.

line

str conj_peters.line = 0

Definition at line 285 of file conj_peters.py.

ee

conj_peters.ee = []

Definition at line 287 of file conj_peters.py.

G

conj_peters.G = Box(ND, o)

Definition at line 289 of file conj_peters.py.

T

conj_peters.T

Definition at line 290 of file conj_peters.py.

nfb

conj_peters.nfb

Definition at line 290 of file conj_peters.py.

prev

list conj_peters.prev = ee[0]

Definition at line 294 of file conj_peters.py.

flush

conj_peters.flush

Definition at line 295 of file conj_peters.py.