Extending the robustness and efficiency of artificial compressibility for partitioned fluid–structure interactions

Abstract

In this paper we introduce the idea of combining artificial compressibility (AC) with quasi-Newton (QN) methods to solve strongly coupled, fully/quasi-enclosed fluid–structure interaction (FSI) problems. Partitioned, incompressible, FSI based on Dirichlet–Neumann domain decomposition solution schemes cannot be applied to problems where the fluid domain is fully enclosed. A simple example often provided in literature is that of a balloon with a prescribed inflow velocity. In this context, artificial compressibility (AC) is a useful method by which the incompressibility constraint can be relaxed by including a source term within the fluid continuity equation. The attractiveness of AC stems from the fact that this source term can readily be added to almost any fluid field solver, including most commercial solvers. Once included, both the modified fluid solver and structural solver can be treated as “black-box” field operators. AC is however limited to the class of problems it can effectively be applied to. For example, AC is an efficient solution strategy for the simulation of blood flow through arteries, but performs poorly when applied to the simulation of blood flow through an opening heart valve. The focus of this paper is thus to extend the application of AC by including an additional Newton system accounting for the missing interface sensitivities. We do so through the use of a multi-vector update quasi-Newton (MVQN) method, where the required system Jacobians are approximated rather than explicitly computed. In so doing, we continue to facilitate the notion that the AC modified fluid field solver and solid field solver can be treated as “black-box” solvers. We aim to demonstrate the improved performance of the combination of AC+QN when compared to AC applied in isolation.