A numerical comparison of some Multiscale Finite Element approaches for convection-dominated problems in heterogeneous media

TL;DR

This paper compares various Multiscale Finite Element methods for advection-diffusion problems in heterogeneous media, focusing on their performance in advection-dominated regimes to identify effective approaches.

Contribution

It provides a comprehensive numerical comparison of classical, stabilized, and splitting MsFEM approaches for advection-dominated multiscale problems.

Findings

Adjusted MsFEM methods improve accuracy in advection-dominated regimes

Stabilized MsFEM variants enhance numerical stability

Splitting methods effectively handle multiscale diffusion and strong advection

Abstract

The purpose of this work is to investigate the behavior of Multiscale Finite Element type methods for advection-diffusion problems in the advection-dominated regime. We present, study and compare various options to address the issue of the simultaneous presence of both heterogeneity of scales and strong advection. Classical MsFEM methods are compared with adjusted MsFEM methods, stabilized versions of the methods, and a splitting method that treats the multiscale diffusion and the strong advection separately.