An Iterative Decoupled Algorithm with Unconditional Stability for Biot Model

TL;DR

This paper introduces an iterative decoupled algorithm for the Biot model that guarantees unconditional stability and convergence without additional assumptions, demonstrated through numerical experiments.

Contribution

The paper proposes a novel iterative decoupled algorithm for the Biot model with unconditional stability and convergence analysis based on a 3-field formulation.

Findings

Algorithm converges without extra assumptions

Numerical experiments confirm accuracy and efficiency

3-field formulation improves decoupling stability

Abstract

This paper is concerned with numerical algorithms for Biot model. By introducing an intermediate variable, the classical 2-field Biot model is written into a 3-field formulation. Based on such a 3-field formulation, we propose a coupled algorithm, some time-extrapolation based decoupled algorithms, and an iterative decoupled algorithm. Our focus is the analysis of the iterative decoupled algorithm. It is shown that the convergence of the iterative decoupled algorithm requires no extra assumptions on physical parameters or stabilization parameters. Numerical experiments are provided to demonstrate the accuracy and efficiency of the proposed method.