A multicomponent iterative method of domain decomposition on adaptive grids for solution of two‐dimensional heat transfer equation is proposed. The adaptive grid is constructed in curvilinear space where Cartesian grid is non‐stationary and depends on the solution behavior. In curvilinear space the initial two‐dimensional heat transfer equation is converted to the system of nonlinear parabolic equations with mixed derivatives, a source and convective transfer.
Dvimatinės šilumos laidumo lygties sprendimas judančiuose tinkluose daugiakomponentiniu iteraciniu metodu
Santrauka. Darbe nagrinėjamas daugiakomponentinis iteracinis metodas, kuriuo sprendžiamas dvimatis šilumos laidumo uždavinys. Naudojamas adaptyvus diskretusis tinklas ir skaičiavimo sritis skaidoma į atskiras nepriklausomas dalis. Adaptyvusis tinklas konstruojamas kreivinėse koordinatėse ir jis priklauso nuo uždavinio sprendinio. Po transformacijos gaunama netiesinių skirtumų lygčių sistema tenkinanti paraboliškumo sąlygą. Lygtyje atsiranda nariai su mišriomis išvestinėmis, konvekcijos nariai ir šilumos šaltiniai. Gautoji lygčių sistema sprendžiama panaudojant srities skaidymo ir daugiakomponentinių iteracinių metodų kombinaciją.
Sytova, S. (2000). Multicomponent iterative method for solving two‐dimensional heat transfer equation on moving grids. Mathematical Modelling and Analysis, 5(1), 164-174. https://doi.org/10.3846/13926292.2000.9637139
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