Added Mass Partitioned Fluid–Structure Interaction Solver Based on a Robin Boundary Condition for Pressure

Abstract

This paper describes a self-contained, partitioned fluid–structure interaction solver based on a finite volume discretisation. The incompressible fluid flow is described by the Navier–Stokes equations in the arbitrary Lagrangian–Eulerian form and the solid deformation is described by the St. Venant-Kirchhoff hyperelastic model in the total Lagrangian form. Both fluid and solid are discretised in space using the second-order accurate cell-centred finite volume method, and temporal discretisation is performed using the first-order accurate implicit Euler scheme. Coupling between fluid and solid is performed using a Robin-Neumann partitioned procedure based on a new Robin boundary condition for pressure. The solver has been tested on the wave propagation in an elastic tube test case characterised by a low solid-to-fluid density ratio. The first-order temporal accuracy is shown and the stability of the method is demonstrated for both the strongly coupled and loosely coupled versions of the solution procedure. It is also shown that the proposed methodology can efficiently handle FSI cases in which the fluid domain is entirely enclosed by Dirichlet boundary conditions, even for the case of geometrically nonlinear elastic deformation.