Flud Flow Smulton wth Cellulr Automt 00N2100008J 2002 225
1. cellulr utomton n t+ 1 t t = f( r, L, + r (1 t t+ 1 f t r t +1 Prllel Vrtul Mchne Messge-Pssng Interfce 1
2. 2. 1 t t 0 t = 1 = 1 = t = 2 2
(2 t t t 2 1 k k t r 1 + 1 t + r t r t + 1 + 3
f = f(,, L,, L, 1 t+ 1 t t t t t r r+ 1 + r + r (2 t + 1 t r =1 t+ 1 t t = 1+ + 1 mod 2 (3 (3 t t +1 111 110 101 100 011 010 001 000 0 1 0 1 1 0 1 0 01011010 01011010 90 (390 90 t t +1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 0 * 1 0 1 1 0 1 0 0 0 0 0 1 1 1 * 8 2 = 256 n r k n= k + 2 1 r = 2 t +1 4
= f(,,,, t+ 1 t t t t t 2 1 + 1 + 2 (4 5 2 = 32 32 2 ~ 40 t+ 1 t = f( (5 + r 6 2 = 64 t + 1 t 2 r= 2 64 5
k = 2 S 6
1 ( 4 1 ( 3 0 ( t t S S + = = = (6 lttce gs utomton, LGA 2. 2 7
Lttce Boltzmnn, LB 2. 3 8
HrdyPoumeuPzzs n ( nnnn 1, 2, 3, 4 t t +1 n ( x+ c, t+ 1 ( x,t ( ( ( n n x+ c, t+ 1 = n x, t + n x, t = 1, K, 4. (7 c n ( x, t ( n n n ( 1 n ( 1 n nn ( 1 n ( 1 n = + 1 + 3 + 2 + 2 + 1 + 3 (8 + b ( b 90 9
(, 2 + 2. 4 FrshHslcherPoumeu ( 10
FHP-I FHP-II FHP-III 11
( = n n t x 1, 2, L, 6 n( x, t = { n ( x, t : = 1,2, L,6} (b ( n n n n n n n=,,,,, = (1, 0,1,1, 0, 0 (10 1 2 3 4 5 6 (9 n x, t = n x, t : = 0,1,2, L,6} (11 ( { ( 1/2 (9 12
t t + 1 n x+ c, t+ 1 n ( x, t ( ( ( ( n, x+ c, t+ 1 = n x, t + n x, t = 1, 2, L, 6 (12 ( 3 ( 2 ( 3 ( ( ( π π c = = cos / 3,sn / 3, = 1, 2, L, 6 n ( x, t ( 2 ( ( = + (13 (8 ( 2 ( = ( x, t n+ 1n+ 4( 1 n( 1 n+ 2( 1 n+ 3( 1 n+ 5 { 1 ( x, } ( 1 ( 1 ( 1 ( 1 ( ( ( ( + t n n n n n n + 1 + 5 + 1 + 3 + 4 nn 1 n 1 n 1 n 1 n ( x, t + 3 + 1 + 2 + 4 + 5 0 = 1 ( 3 ( ( ( ( ( ( ( = n n n 1 n 1 n 1 n nn n 1 n 1 n 1 n + 1 + 3 + 5 + 2 + 4 + 2 + 4 + 1 + 3 + 5 13
s( = { s = 0or1, = 1,2, L, b} s' = s' = 0or1, = 1,2, L, b ( { } ss, ' s s ' A s s' s s ' 2 b b = 6 64 s s ' = 1, s(14 ss, ' ss, ' ' s s ' ss, ss, ' ' n ( x+ c, t+ 1 ss, n ( x, t s ( ( ( 1 s n x+ c, t+ 1 = s ' n 1 n (15 s, s' ss, ' s ( ( ( 1 s, 1 x = n t s n n s (15 (16 t (16 s ( ( ( ( ( 1 s, 1, ' 1 = n x+ c t+ n x t = s s n n (17 s, s' ss, ' (12 (17 s ( ( ( ( ( 1 s, 1, ' 1 + + = + n x c t n x t s s n n (18 s, s' ss, ' ( + + = ( n x c, t 1 n x, (19 ( + + = ( t cn x c, t 1 cn x, (20 (12 ( N = n ( ( ( N x+ c, t+ 1 = N x, t + N x, t (21 ( 1,2,, N = (22 L N = b s ( ( ( ( 1 s, ' 1 t s s A N N N x = s s' ss, ' s s' s, s', (23 A = s, s' (24 14
N (19 (20 N ( x+ c, t+ 1 = N ( x, t (25 ( + + = ( t c N x c, t 1 c N x, (26 (14 A = 1 (27 s' s s' (14 s s ' sem-detled blnce A = s' (28 s s s' 1 N x+ c, t+ 1 N (, ( (23 x t (, t N ( x, t (21 s ( ( ( ( 1 s, ' 1 t s s A N N N x = s s' ss, ' (, t ( 1 N N x = 0 =0 (29 N N% (30 1 N N x s = ( s ' s As s' N% = 0 (31 ss, ' (31log N % s ' N% s As s' log 0 s ss, ' = N N% (32 % N% s ' s log N% = log N% ( s ' s s s' s s s' (33 A = A ' = 1(34 s 15
% % = 0 (35 s s' As s' N N ss, ' (32 (35 ~ s ' N log N = 0 (36 ~ s ~ s ~ s' A s s', ' ~ s N + N ss N x y t ylog + y x= log dt 0 (37 x y x x= y(36 (37 A s s ' s ' N % = N% s (38 s s ' ( ( ' log N% s' s As s = 0 (39 (39 log N % ρ u h q ( log N % = h+ qc (40 ( } N% = exp{ h+ qc (41 (30 N N = N% 1 N 1 N% = 1+ exp + ( h qc eq (42 eq N n N ( ( n = ρ x, t = N x, t (43 ( ( u x, t = c N x, t / ρ (44 16
( 0 N eq (21 N ( = N ( ( ( ( ( 0 1 2 N = N x, t + εn x, t + O ε (45 (25 (26 ρ + = t ( ρu 0 (46 ρu + P= S+ (47 t P S P S ρ ρu β + = 0 (48 t β x β ρu Pα β S α + = t β x β x αβ αβ αβ (49 u P c g g u u c 2 2 αβ = s ρ 1 ( ρ δ 2 αβ + ρ ( ρ α β (50 S αβ ρuβ ρuα 2 ρu = ν( ρ + xα xβ D γ xγ γ δ αβ (51 D α, β b δαβ c s 4 2 bc c ν( ρ = νc( ρ + ν p = φ( ρ D D+ 2 D D+ 2 g ( ρ ( 2 ( ( (52 D b 2 2 ρ c, 2 = cs = (53 D D+ b ρ D 17
φ( ρp α β p P = pδ + ρu u αβ αβ α β u =0 (54 1 + = p + υ t ρ u u u 2 u (55 (55 (48 (49 2 p = c ρ s ρ 0 u =0 (56 2 u 1 2 u + 2 g( ρ0 u u = p cs ρ0g( ρ0 2 + υ( ρ0 u(57 t ρ c g ( ρ 0 ( ( 2 2 2 cs ρ0g( ρ0 ( u / c 2 2 2 cs ρ0g ρ0 u / c t tg ( ρ 0, ( ( ρ υ ρ υ (58 g ρ ( Re υ '( ρ =υ( ρ /g ( ρ ( ρ0 ( 0 0 ( 0 g Re = lu 0 0 (59 υ ρ l0 u0 ( M = u0 / cs ( 0 0 * 0 Re = Ml u R ρ (60 0 18
R ( ρ * 0 ( 0 ( cg ρ s = (61 υ ρ 0 R ( ρ * 0 g υ FHP-I FHP-II FHP-III ρ 0 6d 7d 7d c s 1/ 2 3/7 3/7 g 11 2d 21 d 71 2d 12 1 d 71 2d 12 1 d υ 1 1 1 12 d 8 ( 1 d 3 1 1 1 1 28 d( 1 d 3 4 1 d 8 7 1 1 1 1 28 d( 1 d 8 1 8 ( 1 d 7 19
20481024 u u=0.1 20
21
3. 3. 1 3. 2 ( g ρ c N t x (, f t x N f c = c 3.2.1 1-speed2-speed3-speed dmenson, velocty, 22
1-speed c = = c c = 0,1, 2, L,6 ( 1-speed 2-speed = { σ, }, ( = 0,1, L,6 c ( σ=0,1, 2 σ c c ( 1, ( = c = 2 2, c 2-speed 23
3-speed { σ, } ( σ= ( = 0,1, L,6 =, 0,1, 2,3, c c ( 1, ( = c = 2 2, c 3-speed = c { σ, } = σ c σ = 0,1, 2, L c ( ( = 0,1, 2, L,6 3.2.2 24
((b p p = 1 p = 2 2 = { p, } ( p sub lttce = 0,1, 2 ( 0,1, L, 4 c c ( 1, ( = c = 2 2, c 25
Qn { p, k, } =, 0,1, 2, k ( p = ( = 0,1, L, 4 ( = 0,1, 2 ( ( ( ( ( p k pk, = 0,0,1,1,1,2,2,1 c = k pc Chen { p, k, } ( p = ( k = ( = 0,1, L, 4 ( ( ( ( ( =, 0,1, 2, 0,1, 2, p k pk, = 0,0, 1,2, 2,1, 2,2 c = k pc 26
3.2.3 p =1, 2, 3 { p, k, } = p k ( pk, = ( 0,0,( 1,2,( 3, 1 c ( 1,2, = 2c = 3 3,1, c ( c 3. 3 (21N f c c (, 1 (, (, f x+ c t+ = f x t + f x t (62 27
= 0 (62 c = 0 (63 c = 0 (64 2 1 eq f( x + c, t + 1 = f( x, t f(, t f (, τ x x t (65 τ f ( x, t 1/ τ ( x, t τ τ eq f (A D g ( ρ eq f ( f = A+ B + C + D eq 2 2 c u c u u (66 g ρ f f ' f' = f 1τ ( f f eq ' ' f f f ( eq 28
f f ρ u eq f ρ u ε (66 ( A D eq 2 0, eq ( ρ ξ f ρ 1 2 1 2 = + + 2( 6 3 c u c u u (69 2 (69 ε uα uα p µ ρu γ ρ ρ uβ uα ρ + ρuβ = + + uα + uβ + ς + (71 t x β x α xα ρ xγ xβ x α x β xα x β p µ ς α γ β ( ξ ( 2τ 1 τ ( 1 ξ 1 p = ρ, cs = 1 /2, µ =, ς = 2ξ 1 ρ/4 (72 2 8 2 (69 (69 eq N eq ρ= f ( x, t (67 ( eq u= c f x, t / ρ (68 (65 (66 f = ξρ ρu ρ ρu + α = 0 (70 t x ξ α 29
3. 4 (12 ( ( n x+ c t, t+ t = n x, t + (73 t (12 f + v f = Q (74 t Q (73 2 n( x+ c t, t+ t = n( x, t + t n + c t n + O ( t (75 t n f, c v, / t Q n + c n = (76 t t f + = t τ 1 eq v f ( f f f f ( xv,, t ( (77 v f ( x, t f 1 + eq v f = ( f f (78 t τ L U n t r c v F ˆ 1 + c F = ( F F tˆ τε ˆ eq (79 c = v / U = ˆ L t ˆ = t U / Lτ ˆ = τ / t c F = f / nr ε U ε= tc L ε (79 30
( x ˆ, ˆ+ ˆ ( x ˆ, ˆ ( x ˆ + ˆ, ˆ+ ˆ ( x ˆ, ˆ+ ˆ F t t F t F x t t F t t + cx tˆ xˆ 1 = τε ˆ tˆ = t U / L ( x ˆ +, ˆ+ ˆ ( x ˆ, ˆ+ ˆ ( x ˆ +, ˆ+ ˆ ( x ˆ, ˆ+ tˆ F y t t F t t F z t t F t + cy + cz y z eq ( F F (80 ( ( ( ( ( xˆ / tˆ = c F ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ x, t + t F x, t F x+ c t, t + t F x, t + t + tˆ tˆ F ( ˆ ˆˆ, ˆ ( ˆ, ˆ x+ c t t + t F x t 1 eq = = ( F F tˆ τε ˆ (81 t = t ˆt 1 eq F( x+ c t, t+ t F( x, t = ( F F (82 τ c 31
4. 4. 1 4.1.1 symmetrc multprocessor, SMP Hgh-performnce Fortrn 4.1.2 4.1.3 4.1.4 32
4. 2 1 p p T E pt = (83 (83 T T p 1 p p ( ( 1 1 p R f f f R = + (84 33
f p ( R f R 50 34
4. 3 4.3.1 4.3.2 Domn Decomposton 4.3.3 prtcle method nner loop 4. 4 4.4.1 35
Messge Pssng Interfce Prllel Vrtul Mchne 1997 MPI-1 MPI-2 UNIX UNIX Wndows TCP/IP 4.4.2 36
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5. [1] Bsten Choprd, nd Mchel Dro. Cellulr Automt Modelng of Physcl System. Cmbgdge Unversty Press, 1999. [2] Deter A.Wolf-Gldrow. Lttce-Gs Cellulr Automt nd Lttce Boltzmnn Models. Sprnger, 2000. [3] Dnel H.Rothmn, nd Stephne Zlesk. Lttce-Gs Cellulr Automt. Cmbrdge Unversty Press, 1997. [4].., Vol.77, No.2, pp.197-232,2001. [5]..... 1999. [6]..... 1998. [7]... 1994. [8]... 1994. [9] P.... 2001. 38