Test Suite for PDE's

Diffusion-Advection-Reaction Equation

No.	a	b	c	Solution	Domain (2D)	Domain (3D)
0	1	0	0	cos(½πx) cos(½πy) cos(½πz)	2	2
1	1	0	0	e^xe^ye^z	0	0
2	1	0	0	cos(½πx) cos(½πy) cos(½πz)	6	6
3	1	0	0	r²	2	2
4	1	0	0	r²	20	40
5	1	0	0	sin(½πx) sin(½πy) sin(½πz)	9	-
8	1	0	0	cos(½πx) cos(½πy) cos(½πz)	8	-
9	1	0	0	cos(½πx) cos(½πy) cos(½πz)	9	-
10	1	0	0	e^xe^ye^z	20	40
11	1	0	0	e^xe^ye^z	9	-
30	1	0	0	r^2/3sin(2/3φ)	10	-
31	1	0	0	r^1/2sin(1/2φ)	12	-

50				???	0	0
100	ν	Kovasznay 1	0	Tracer in Kovasznay velocity field	4	-
200	ν	b_circ	0	e^xe^ye^z	0	0
201	ν	(1,0)^T	0	e^xe^ye^z	0	0
202	ν	b_cos	0	e^xe^ye^z	0	0
203	ν	b_pillow	0	e^xe^ye^z	0	0
250	ν	β	0	Riemann problem, jump at (0,0,0)	6	6
251	ν	β	0	Riemann Problem, jump at (½,½,½)	6	6
300	ν	0	1	layer	50	50
2000	1. 10	0	0	(x>0) ? x : 10x	2	2
2001	1. 10	0	0	(x.v₁>0) ? x : 10x	2	2

b_circ = ()^T
b_cos = (cos(π/5), sin(π/5))^T
b_pillow = 2((2y-1)(1-(2x-1)²), -(2x-1)(1-(2y-1)²))^T
v₁ = (sin(π/6), cos(π/6))^T

No.	ν	μ	λ	Solution	Domain (2D)	Domain (3D)
0	1	0	0	sin(½πx) sin(½πy) sin(½πz) sin(πx) sin(πy) sin(πz) sin(3/2πx) sin(3/2πy) sin(3/2πz)	2	2
1	ν	0	0	e^xe^ye^z	0	0
2	1	0	0	sin(½πx) sin(½πy) sin(½πz) sin(πx) sin(πy) sin(πz) sin(3/2πx) sin(3/2πy) sin(3/2πz)	6	6
20	ν	μ	λ	-y 0 2y	2	2
21	ν	μ	λ	-y 0 2y	50	50
1000	ν	0	0	e^xe^ye^z	0	0
2000					2	2
2100					2	2

No.	Viscosity	Solution	Domain (2D)	Domain (3D)
0	0	u = p = cos(pix) cos(piy)	2	2
1	0	e^xe^ye^z	2	2
8	0	u = x, v = -y	2
9	0	u_i = x_(i+1)%d	2	2
10	∞	Poisseuille	40	40
11	ν	Poisseuille	40	40
12	∞	Poisseuille	40	40
13	ν	Poisseuille	40	40
15	∞	Poisseuille	41	41
16	ν	Poisseuille	41	41
17	∞	Poisseuille	41	41
18	ν	Poisseuille	41	41
20	∞	Poisseuille	2	2
21	ν	Poisseuille	2	2
22	∞	Poisseuille	2	2
23	ν	Poisseuille	2	2
25	∞	Poisseuille	5	5
26	ν	Poisseuille	5	5
27	∞	Poisseuille	5	5
28	ν	Poisseuille	5	5
100	ν	Kovasznay	5
101	ν	Kovasznay	4
200	ν		0
1000	ν	Backward facing step	1000
1001	ν	Backward facing step	1001
1010	ν	Backward facing step	1000
1200	ν	Benchmark 30	1200
1201	ν	Benchmark 30	1201
1205	ν	Benchmark 30	1205
1206	ν	Benchmark 30	1206
1207	ν	Benchmark 30	1207
1208	ν	Benchmark 30	1208
1210	ν	Benchmark 30	1200
1211	ν	Benchmark 30	1201
1250	ν		2000
1251	ν		2000
1252	ν		2000

Order of colors, starting with zero:

Number	2D	3D	boundary condition
0	[0,1]^d
1	[0,π]^d
2	[-1,1]^d
3	[-π,π]^d
4	[-.5,1.5]^d
5	[-.5,1.5]^d		Neumann at x=1.5
6	[0,1]^d		Neumann at x=0 and y=0 and z=0
7	[-1,1]^d		Neumann at x=1
8	[-1,1]², hyper-ball grid
9	[-1,1]²,
10	L-shaped, [-1,1]
11	L-shaped, [-π,π]
12	slit cube, [-1,1]
13	slit cube, [-π,π]
20	circle around origin, r=1
21	circle around origin, r=π
22	circle around (1,2), r=1
23	circle around (1,2), r=π
30	shell around origin, r1=.5, r2=1
31	shell around origin, r1=.1, r2=1
32	shell around origin, r1=.01, r2=1
40	[-1,1]²	cylinder r=1, h=1
41	[-1,1]²	cylinder r=1, h=1	Neumann at x=1
50	[-1,1]^d		Dirichlet at x=-1 and x=1
1000
1001
1200
1201
2000