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

Abstract

In this work, we propose and analyze Crank-Nicolson-type iterative decoupled algorithms for a three-field formulation of Biot’s consolidation model using total pressure. These algorithms are derived from an equivalent, reformulated fully coupled system based on the Crank-Nicolson method, which is then decomposed using an iterative decoupled strategy. Two variants are introduced, differing in the solving order of temporal computation and iteration: a time-stepping and a global-in-time approach. The latter is particularly notable for its potential for parallel-in-time computing, offering an efficient approach for long-time simulations. Capitalizing on the properties of the underlying methods, both algorithms are proven to achieve second-order accuracy in time and unconditional stability. Through numerical experiments, we validate theoretical predictions and demonstrate the effectiveness and efficiency of these novel approaches.