Contrast-Independent Partially Explicit Time Discretizations for Quasi Gas Dynamics

Boris Chetverushkin, Yalchin Efendiev and Wing Tat Leung
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Boris Chetverushkin: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047 Moscow, Russia
Yalchin Efendiev: Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
Wing Tat Leung: Department of Mathematics, University of California, Irvine, CA 92697, USA

Mathematics, 2022, vol. 10, issue 4, 1-16

Abstract: In the paper, we study a design and stability of contrast-independent partially explicit time discretizations for Quasi-Gas-Dynamics (QGD) Equations in multiscale high-contrast media. In our previous works, we have introduced contrast-independent partially explicit time discretizations. In this paper, we extend these ideas to multiscale QGD problems. Because of high contrast, explicit methods require a very small time stepping. By designing appropriate spatial splitting and temporal splitting, partially explicit methods remove this constraint. The proposed partially explicit time discretization consists of two steps. First, we split the space into contrast dependent (fast) and contrast independent (slow) components on a coarse grid that is much larger compared to spatial heterogeneities. Secondly, we design a temporal splitting algorithm in a such way that it is stable and the time step is independent of the contrast and only depends on the coarse mesh size. Using proposed method, a few degrees of freedom are treated implicitly and the approach is mostly explicit. We prove that the proposed splitting is unconditionally stable under some suitable conditions formulated for the second space (slow). We present numerical results and show that the proposed methods provide results similar to implicit methods with the time step that is independent of the contrast.

Keywords: multiscale method; quasi-gas dynamics; temporal splitting; CEM-GMsFEM; explicit-implicit (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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