Crank-Nicolson-type iterative decoupled algorithms for Biot's consolidation model using total pressure

TL;DR

This paper introduces new Crank-Nicolson-type iterative decoupled algorithms for Biot's consolidation model, achieving second-order accuracy and unconditional stability, with one algorithm supporting parallel-in-time computation.

Contribution

The paper develops two novel iterative decoupled algorithms for Biot's model, including a global-in-time method with parallel-in-time features, enhancing computational efficiency.

Findings

Both algorithms are second-order accurate in time.

They demonstrate unconditional stability in numerical tests.

The global-in-time algorithm enables parallel-in-time computation.

Abstract

In this work, we develop Crank-Nicolson-type iterative decoupled algorithms for a three-field formulation of Biot's consolidation model using total pressure. We begin by constructing an equivalent fully implicit coupled algorithm using the standard Crank-Nicolson method for the three-field formulation of Biot's model. Employing an iterative decoupled scheme to decompose the resulting coupled system, we derive two distinctive forms of Crank-Nicolson-type iterative decoupled algorithms based on the order of temporal computation and iteration: a time-stepping iterative decoupled algorithm and a global-in-time iterative decoupled algorithm. Notably, the proposed global-in-time algorithm supports a partially parallel-in-time feature. Capitalizing on the convergence properties of the iterative decoupled scheme, both algorithms exhibit second-order time accuracy and unconditional stability. Through numerical experiments, we validate theoretical predictions and demonstrate the effectiveness and efficiency of these novel approaches.