The Heterogeneous Multiscale Finite Volume Method for Convection-Diffusion-Reaction Problem
Tao Yu, Haitao Cao
TL;DR
This paper introduces a multiscale finite volume method combining heterogeneous multiscale techniques to efficiently solve convection-diffusion-reaction problems, achieving optimal convergence rates in periodic media.
Contribution
The paper develops a novel HMM-based finite volume method tailored for multiscale convection-diffusion-reaction equations, demonstrating optimal convergence in periodic settings.
Findings
Achieves optimal order convergence in H^1-norm
Effective for multiscale convection-diffusion-reaction problems
Validated in periodic media
Abstract
In this paper, we employ an finite volume method (FVM) based on the heterogenous multiscale method (HMM), for the multiscale convection-diffusion-reaction problem. The optimal order convergence rate in H^1-norm is given for periodic medias.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Advanced Numerical Methods in Computational Mathematics · Composite Material Mechanics