Iterative Coupling for Fully Dynamic Poroelasticity

TL;DR

This paper introduces an iterative coupling scheme for simulating fully dynamic poroelasticity, proving its convergence and relating it to existing quasi-static methods, thus advancing numerical approaches for complex coupled systems.

Contribution

It develops a convergent iterative scheme for fully dynamic poroelasticity and connects it to established quasi-static methods, broadening numerical tools for these systems.

Findings

Proves convergence of the iterative scheme in Banach spaces.

Recasts the semi-discrete solution as an energy minimizer.

Links the scheme to the undrained split in quasi-static Biot systems.

Abstract

We present an iterative coupling scheme for the numerical approximation of the mixed hyperbolic-parabolic system of fully dynamic poroelasticity. We prove its convergence in the Banach space setting for an abstract semi-discretization in time that allows the application of the family of diagonally implicit Runge-Kutta methods. Recasting the semi-discrete solution as the minimizer of a properly defined energy functional, the proof of convergence uses its alternating minimization. The scheme is closely related to the undrained split for the quasi-static Biot system.