Multicontinuum homogenization and its relation to nonlocal multicontinuum theories

TL;DR

This paper develops a general framework for multicontinuum homogenization, introduces cell problem formulations with oversampling techniques to reduce boundary effects, and explores their relation to nonlocal multicontinuum theories.

Contribution

It provides a unified derivation of multicontinuum equations, innovative cell problem formulations, and links to nonlocal approaches, advancing multiscale modeling methods.

Findings

Oversampling reduces boundary effects in cell problems.

Different constraint choices impact homogenization accuracy.

The methods relate to and extend nonlocal multicontinuum theories.

Abstract

In this paper, we present a general derivation of multicontinuum equations and discuss cell problems. We present constraint cell problem formulations in a representative volume element and oversampling techniques that allow reducing boundary effects. We discuss different choices of constraints for cell problems. We present numerical results that show how oversampling reduces boundary effects. Finally, we discuss the relation of the proposed methods to our previously developed methods, Nonlocal Multicontinuum Approaches.