Numerical simulation of multiphase multicomponent flow in porous media: Efficiency analysis of newton‐based method
Imankulov T. Lebedev D. Matkerim B. Daribayev B. Kassymbek N.
October 2021MDPI
Fluids
2021#6Issue 10
Newton’s method has been widely used in simulation multiphase, multicomponent flow in porous media. In addition, to solve systems of linear equations in such problems, the generalized minimal residual method (GMRES) is often used. This paper analyzed the one‐dimensional problem of multicomponent fluid flow in a porous medium and solved the system of the algebraic equation with the Newton‐GMRES method. We calculated the linear equations with the GMRES, the GMRES with restarts after every m steps—GMRES(m) and preconditioned with Incomplete Lower‐Upper factorization, where the factors L and U have the same sparsity pattern as the original matrix—the ILU(0)‐GMRES algorithms, respectively, and compared the computation time and convergence. In the course of the research, the influence of the preconditioner and restarts of the GMRES(m) algorithm on the computation time was revealed; in particular, they were able to speed up the program.
GMRES , GMRES (m) , ILU‐GMRES , Krylov subspace method , Multicomponent flow , Newton’s method
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Computer Science Al‐Farabi, Kazakh National University, Almaty, 050040, Kazakhstan
Astana IT University, Nur‐Sultan, 010000, Kazakhstan
Computer Science Al‐Farabi
Astana IT University
10 лет помогаем публиковать статьи Международный издатель
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