Development and Numerical Analysis of Partitioned Algorithms for Fluid-Elastic / Poroelastic Structure Interaction Problems

This work introduces novel, loosely-coupled and easy-to-implement partitioned algorithms for Fluid-Structure Interaction (FSI) and Fluid-Poroelastic Structure Interaction, based on spatial discretization using the standard Galerkin Finite Element Method, and applying finite difference approximations in time. The methods are also immune to the added-mass effect.

First, we present a new method for FSI, based on operator splitting and the Crank-Nicolson discretization method. We prove its stability and second-order convergence properties, and then demonstrate its applicability to blood flow modeling under physiological conditions.

Next, we introduce two new algorithms for modeling the interaction between a flowing fluid and a viscoelastic material with a fully-saturated porous matrix. Both methods are based on implicit-explicit methods and are also second-order convergent. We prove the stability of each method, and show that one of the methods is uniformly stable over a long period of time. Finally we investigate their behaviors using numerical examples.

Last of all, we introduce a new loosely-coupled partitioned scheme based on generalized Robin interface conditions, using a model in which the coupling conditions account for the flow entry resistance. This partitioned method that we present is applicable for the interaction between a freely-flowing fluid and a fully-saturated poroelastic material. The proposed method is non-iterative and unconditionally stable, and we demonstrate its applicability using numerical examples.