, . . 1 , . . 1 , . . 2 . 1 ( . . ), 2 . ++ , щ ( , ) , , . , , щ щ ) , , , . . . щ щ . ( . , , . , . . щ . , OpenFOAM, . . , щ ё . , . , Ax = b , A – , (1) n 1 , x – nn , b – n 1 . щ 0 = Ax b A (1). x = (I A)x b , . . x = (I A)x b k 1 k , (2) , (3) k- (k+1)- μ ( 230 №"β.βγγ5.β014/K"). e xx , k k (β) xx = (I A)(x x ) k 1 k , (4) e = (I A)e k 1 k e = Me k 1 k (5) , , μ (M) 1 , e xx k 1 k 1 (γ) (4) (5) , e , . . M (1). , . , M ii M ij , i 1,2,..., n. μ M nn (6) i j d i M ij . Di z ]:| z Mii di j i M. . i, ( di , , ДβЖ. M ii M ii ). Fi mii mij , (7) i j i 1, 2,..., n . , F: Fi Fi normalised max(Fi ) (0;1Ж F OpenFOAM. щ 0. Fi 1, - , щ (8) , Fi F . , ДγЖ. laplacianFoam OpenFOAM, . T, Refinement - AMR T), laplacianFoamF. , (Adaptive Mesh F (6) , 231 – (AMR F). . . . , Z X 100 1, , Y 10 1- μ grad(T) = 10. . . 5 T = 1 C; щ xy, z=0μ , μ . μ T 2T 0 t , ,t T - , β , (9) . , AMR F . AMR T. β- , AMR F AMR T AMR F 3. γ- , 232 . T1 573C , γ T2 273C . 0, . . , ( ). F ( . 4). , - (1), A. , b 4 - AMR F T , « » . , 5 - AMR T , « AMR F, 5 AMR T. 6. 6- AMR F, AMR T 233 « » AMR FT. » 6, AMR FT . AMR T щё , AMR F , . , , , щ . . – AMR T , . , AMR T. 1. . . . : , 1977 2. Brakken-Thal P. GОrsСРorТЧ’s TСОorОЦ Пor EstТЦКtТЧР EТРОЧvКХuОs. Д http://buzzard.ups.edu/courses/2007spring/projects/brakkenthal-paper.pdf γ. Д Ж СЭЭЩЬμ//РТЭСЮЛ.МШЦ/У-avdeev/laplacianFoamF 234 Ж