A stable FSI algorithm for light rigid bodies in compressible flow

TL;DR

This paper introduces a stable partitioned algorithm for fluid-structure interaction involving light rigid bodies in compressible flow, overcoming added mass instability even for bodies with zero mass, validated through analysis and numerical simulations.

Contribution

The paper presents a novel stable FSI algorithm that handles zero-mass bodies in compressible flow using characteristic projection, extending previous methods to more challenging scenarios.

Findings

Proven stability for zero-mass bodies via normal mode analysis.

Numerical simulations demonstrate effectiveness in 2D shock impact problems.

Revealed the form of added mass tensors based on fluid impedance.

Abstract

In this article we describe a stable partitioned algorithm that overcomes the added mass instability arising in fluid-structure interactions of light rigid bodies and inviscid compressible flow. The new algorithm is stable even for bodies with zero mass and zero moments of inertia. The approach is based on a local characteristic projection of the force on the rigid body and is a natural extension of the recently developed algorithm for coupling compressible flow and deformable bodies. Normal mode analysis is used to prove the stability of the approximation for a one-dimensional model problem and numerical computations confirm these results. In multiple space dimensions the approach naturally reveals the form of the added mass tensors in the equations governing the motion of the rigid body. These tensors, which depend on certain surface integrals of the fluid impedance, couple the translational and angular velocities of the body. Numerical results in two space dimensions, based on the use of moving overlapping grids and adaptive mesh refinement, demonstrate the behavior and efficacy of the new scheme. These results include the simulation of the difficult problem of a shock impacting an ellipse of zero mass.