In this paper we consider a filtration problem in a rectangle or a perturbed rectangle region with an essential nonlinearity and high values of velocity. The conservative averaging method with quadratic or rational approximation over the rectangle thickness gives us 1D problem instead of the original 2D problem. This ID solution can be used as an initial approximation for the original 2D problem. The conservative averaging method is considered and results of some numerical experiments are presented.
Filtracijos uždavinio su dideliaias greičiais sprendimas konservatyviu vidurkinimo metodu
Santrauka. Straipsnyje sprendžiamas dvimatis filtracijos uždavinys. Sritis yra stačiakampė arba deformuota stačiakampė. Nagrinėjamas atvejis, kai skysčio tekėjimo greitis yra didelis ir būtina naudoti netiesinį matematinį modelį. Panaudojant vidurkinimo metodą y koordinates kryptimi sprendinys aproksimuojamas parabole, o lygtis yra vidurkinama. Gautoji vienmatė difuzijos‐konvekcijos lygtis yra sprendžiama skaitiškai. Taip sudarytas sprendinys ne visada yra monotoniškas, todėl nagrinėjamas ir dar vienas artinys, kuris aprašomas racionalia trupmena. Pateikti skaičiavimo eksperimento rezultatai, gauti sprendžiant uždavinį dviem atvejais, kai vyrauja konvekcijos procesas arba difuzijos procesas. Algoritmo ir iteracinio proceso konvergavimas nėra ištirtas.
Jegorov, J., & Buikis, A. (2001). Application of the conservative averaging for the filtration problem with large velocity. Mathematical Modelling and Analysis, 6(2), 251-261. https://doi.org/10.3846/13926292.2001.9637164
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