Computational multiscale methods for linear heterogeneous poroelasticity

TL;DR

This paper introduces a multiscale numerical method for efficiently solving linear heterogeneous poroelasticity problems, leveraging local orthogonal decomposition to handle rapidly oscillating parameters with proven optimal convergence.

Contribution

The paper develops a novel multiscale method based on local orthogonal decomposition for poroelasticity, considering the full system to improve accuracy and efficiency.

Findings

Proves optimal first-order convergence of the method.

Numerical experiments confirm theoretical results.

Decouples displacement and pressure corrector problems.

Abstract

We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough numerical treatment. In this paper, we propose a method based on the local orthogonal decomposition technique and motivated by a similar approach used for linear thermoelasticity. Therein, local corrector problems are constructed in line with the static equations, whereas we propose to consider the full system. This allows to benefit from the given saddle point structure and results in two decoupled corrector problems for the displacement and the pressure. We prove the optimal first-order convergence of this method and verify the result by numerical experiments.