Mass conservation in the validation of fluid-poroelastic structure interaction solvers

Abstract

Benchmark problems commonly used to test numerical methods for fluid-poroelastic structure interaction often rely on simple examples constructed using the method of manufactured solutions. In this work, we show that such examples are not adequate to demonstrate the performance of the method, especially in cases when the poroelastic system is written in the primal or primal-mixed formulation, and when the dynamics of the poroelastic structure are driven only by dynamic loading from the fluid, which often occurs in biomedical applications. In those cases, the only forcing on the structure comes from the interaction with the fluid at the fluid-structure interface, where the coupling conditions are imposed. One of those conditions is a kinematic condition which enforces the conservation of mass. If this condition is not accurately satisfied, the resulting dynamics might lead to highly inaccurate results in the entire domain. We present three benchmark problems: Example 1 is based on the method of manufactured solutions; Example 2 is based on parameters used in geomechanics; and Example 3 is a benchmark problem with parameters from hemodynamics. Using these examples, we test the performance of the primal, primal-mixed and dual-mixed formulations. While all methods perform well in the first two examples, the primal and primal-mixed formulations exhibit large errors in Example 3, where the densities of the fluid and solid are comparable, and the structure dynamics is purely driven by the fluid loading. To recover the accuracy, we propose to use the primal and primal-mixed methods with a penalty term, which helps to enforce the conservation of mass.