Splitting schemes with respect to physical processes for double-porosity poroelasticity problems

TL;DR

This paper develops and analyzes splitting schemes for double-porosity poroelasticity problems, enabling stable and accurate numerical solutions by separating physical processes and employing finite element methods.

Contribution

It introduces a novel splitting scheme with respect to physical processes for double-porosity poroelasticity problems, ensuring stability and accuracy.

Findings

Schemes are unconditionally stable under certain conditions.

Numerical experiments confirm the accuracy and stability of the proposed methods.

The approach effectively separates displacement and pressure computations.

Abstract

We consider unsteady poroelasticity problem in fractured porous medium within the classical Barenblatt double-porosity model. For numerical solution of double-porosity poroelasticity problems we construct splitting schemes with respect to physical processes, where transition to a new time level is associated with solving separate problem for the displacements and fluid pressures in pores and fractures. The stability of schemes is achieved by switching to three-level explicit-implicit difference scheme with some of the terms in the system of equations taken from the lower time level and by choosing a weight parameter used as a regularization parameter. The computational algorithm is based on the finite element approximation in space. The investigation of stability of splitting schemes is based on the general stability (well-posedness) theory of operator-difference schemes. A priori estimates for proposed splitting schemes and the standard two-level scheme are provided. The accuracy and stability of considered schemes are demonstrated by numerical experiments.