Numerical Modeling of the Fluid-Porohyperelastic Structure Interaction

Abstract

We consider a moving domain, fluid-porohyperelastic structure interaction problem in a dual-mixed formulation. The fluid is described using the Navier--Stokes equations, and the porohyperelastic structure is described using the Biot equations. To solve this problem numerically, we propose two novel, partitioned, loosely coupled methods based on the generalized Robin boundary conditions. In the first partitioned method, the Navier--Stokes problem is solved separately from the Biot problem. In the second proposed method, the problem is further split by separating the Biot problem into a mechanics subproblem and a Darcy subproblem. We derive the energy estimates for the proposed methods on a simplified, linear problem and show that the first partitioned method is unconditionally stable. The second partitioned method is shown to be energy-stable if the structure is viscoelastic and if certain conditions on the problem parameters and the time step are satisfied. The performance of both methods is investigated in the numerical examples.