Nonlocal transport equations in multiscale media. Modeling, dememorization, and discretizations

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

2 Scopus Citations
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Author(s)

  • Yalchin Efendiev
  • Wing Tat Leung
  • Wenyuan Li
  • Sai-Mang Pun
  • Petr N. Vabishchevich

Detail(s)

Original languageEnglish
Article number111555
Journal / PublicationJournal of Computational Physics
Volume472
Online published4 Oct 2022
Publication statusPublished - 1 Jan 2023
Externally publishedYes

Abstract

In this paper, we consider a class of convection-diffusion equations with memory effects. These equations arise as a result of homogenization or upscaling of linear transport equations in heterogeneous media and play an important role in many applications. First, we present a dememorization technique for these equations. We show that the convection-diffusion equations with memory effects can be written as a system of standard convection diffusion reaction equations. This allows removing the memory term and simplifying the computations. We consider a relation between dememorized equations and micro-scale equations, which do not contain memory terms. We note that dememorized equations differ from micro-scale equations and constitute a macroscopic model. Next, we consider both implicit and partially explicit methods. The latter is introduced for problems in multiscale media with high-contrast properties. Because of high-contrast, explicit methods are restrictive and require time steps that are very small (scales as the inverse of the contrast). We show that, by appropriately decomposing the space, we can treat only a few degrees of freedom implicitly and the remaining degrees of freedom explicitly. We present a stability analysis. Numerical results are presented that confirm our theoretical findings about partially explicit schemes applied to dememorized systems of equations.

Research Area(s)

  • CEM-GMsFEM, Multiscale, Partially explicit, Porous media, Transport equations

Citation Format(s)

Nonlocal transport equations in multiscale media. Modeling, dememorization, and discretizations. / Efendiev, Yalchin; Leung, Wing Tat; Li, Wenyuan et al.
In: Journal of Computational Physics, Vol. 472, 111555, 01.01.2023.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review