Design of convergence criterion for fixed stress split iterative scheme for small strain anisotropic poroelastoplasticity coupled with single phase flow

TL;DR

This paper develops a convergence criterion for a fixed stress split iterative scheme in coupled small strain anisotropic poroelastoplasticity and single-phase flow, ensuring the scheme's contractivity.

Contribution

It introduces a novel convergence criterion based on analyzing the difference equations to guarantee iterative scheme convergence in coupled poroelastoplasticity and flow models.

Findings

Established a contractivity-based convergence criterion

Proved the iterative scheme's convergence under the new criterion

Provided a theoretical foundation for stable numerical simulations

Abstract

We arrive at convergence criterion for the fixed stress split iterative scheme for single phase flow coupled with small strain anisotropic poroelastoplasticity. The analysis is based on studying the equations satisfied by the difference of iterates to show that the iterative scheme is contractive. The contractivity is based on driving a term to as small a value as possible (ideally zero). This condition is rendered as the convergence criterion of the algorithm.