Contrast-independent partially explicit time discretizations for multiscale flow problems

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

10 Scopus Citations
View graph of relations

Author(s)

Detail(s)

Original languageEnglish
Article number110578
Journal / PublicationJournal of Computational Physics
Volume445
Online published26 Jul 2021
Publication statusPublished - 15 Nov 2021
Externally publishedYes

Abstract

Many multiscale problems have a high contrast, which is expressed as a very large ratio between the media properties. The contrast is known to introduce many challenges in the design of multiscale methods and domain decomposition approaches. These issues to some extent are analyzed in the design of spatial multiscale and domain decomposition approaches. However, some of these issues remain open for time dependent problems as the contrast affects the time scales, particularly, for explicit methods. For example, in parabolic equations, the time step is dt = H2/κmax, where κmax is the largest diffusivity. In this paper, we address this issue in the context of parabolic equation by designing a splitting algorithm. The proposed splitting algorithm treats dominant multiscale modes in the implicit fashion, while the rest in the explicit fashion. The contrast-independent stability of these algorithms requires a special multiscale space design, which is the main purpose of the paper. We show that with an appropriate choice of multiscale spaces we can achieve an unconditional stability with respect to the contrast. This could provide computational savings as the time step in explicit methods is adversely affected by the contrast. We discuss some theoretical aspects of the proposed algorithms. Numerical results are presented.

Research Area(s)

  • GMsFEM, Multiscale, Multiscale finite element method, Splitting method

Citation Format(s)

Contrast-independent partially explicit time discretizations for multiscale flow problems. / Chung, Eric T.; Efendiev, Yalchin; Leung, Wing Tat et al.
In: Journal of Computational Physics, Vol. 445, 110578, 15.11.2021.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review