Computational multiscale methods for linear heterogeneous poroelasticity
It provides a rigorous numerical framework for geomechanical modeling with rapidly oscillating material parameters.
The paper proposes a multiscale method for linear heterogeneous poroelasticity using local orthogonal decomposition, achieving optimal first-order convergence verified by numerical experiments.
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.