Яндекс.Метрика

S.I. Markov, E.P. Shurina,N.B.Itkina

Выпуск: 2 , Том: 2 , Год издания: 2018
Сериальное издание: Высокопроизводительные вычислительные системы и технологии
Страницы: 70-79

Аннотация

In many applications, one deals with fluid flow in heterogeneous media. Since a natural physical experiment is one of the expensive research technologies, mathematical (computer) modeling is one of the best choices for studying many phenomena. Mathematical modeling of seepage processes is a very complex problem since a real physical medium has a multiscale structure: pores, crocks, caverns. For solving these problems, special numerical methods must be used. We propose a modern mathematical method for simulating seepage processes in heterogeneous anisotropic media. A computational scheme of a multi-scale discontinuous Galerkin method is used for solving a mathematical modeling direct problem of a single-phase seepage process in the heterogeneous anisotropic medium. The proposed computational scheme combines advantages of a classical multiscale finite element method and a high computational flexibility of a discontinuous Galerkin method. For recovering a full effective permeability tensor of the anisotropic heterogeneous medium, we consider an inverse problem using a smoothing Tikhonov functional. The Fletcher-Reeves gradient method is applied for minimizing the smoothing Tikhonov functional and solving the inverse problem of recovering the effective permeability tensor in the heterogeneous anisotropic medium.
индекс в базе ИАЦ: 043025