A Normal Mode Stability Analysis of Numerical Interface Conditions for Fluid/Structure Interaction (Communications in Computational Physics, 2011)
In multi-physics computations where a compressible fluid is coupled witha linearly elastic solid, it is standard to enforce continuity of the normal velocities andof the normal stresses at the interface between the fluid and the solid. In a numericalscheme, there are many ways that velocity- and stress-continuity can be enforced inthe discrete approximation. This paper performs a normal mode stability analysis ofthe linearized problem to investigate the stability of different numerical interface conditionsfor a model problem approximated by upwind type finite difference schemes.The analysis shows that depending on the ratio of densities between the solid andthe fluid, some numerical interface conditions are stable up to the maximal CFL-limit,while other numerical interface conditions suffer from a severe reduction of the stableCFL-limit. The paper also presents a new interface condition, obtained as a simplifiedcharacteristic boundary condition, that is proved to not suffer from any reduction ofthe stable CFL-limit. Numerical experiments in one space dimension show that thenew interface condition is stable also for computations with the non-linear Euler equationsof compressible fluid flow coupled with a linearly elastic solid.