Mathematical analysis of added-mass instability in fluid-structure interaction

When solving fluid-structure interaction (FSI) problems, the so-call artificial added mass effect plays an important role in determining the stability of the computation. We propose a derivation using Von Neumann stability analysis, which shows its significance as a tool for studying this numerical instability. Our derivation demonstrates that FSI solution is severely unstable when density ratio is high, solid structure is thin and flexible. It also shows that this instability can be eliminated by introducing aritificial compressibility.