Corrector estimates and numerical simulations of a system of diffusion-reaction-dissolution-precipitation model in a porous medium

TL;DR

This paper develops and validates a homogenized model for a complex diffusion-reaction system in porous media, providing theoretical justification and numerical comparisons to the microscale model.

Contribution

It introduces a corrector estimate for the homogenized model and performs numerical simulations to compare with the microscale system, advancing modeling accuracy.

Findings

Corrector estimates justify the homogenization approach.

Numerical results show good agreement between effective and microscale models.

The homogenized model effectively captures the system's behavior.

Abstract

A system of diffusion-reaction equations coupled with a dissolution-precipitation model is discussed. We start by introducing a microscale model together with its homogenized version. In the present paper, we first derive the corrector result to justify the obtained theoretical results. Furthermore, we perform the numerical computations to compare the outcome of the effective model with the original heterogeneous microscale model.