Stability estimates and numerical comparison of second order time-stepping schemes for fluid-structure interactions - Wick, Thomas (Numerical Mathematics and Advanced Applications 2011, 2013)
It is well-known that the Crank-Nicolson scheme for pure fluid problems suffers from stability for computations over long-term time intervals. In the presence of fluid-structure interaction in which the fluid equations are reformulated with the help of arbitrary Lagrangian-Eulerian (ALE) mapping, the ALE convection also causes stability problems. In this study, we derive a stability estimate of a monolithically coupled time-discretized fluid-structure interaction problem. Moreover, a numerical comparison of all relevant second order time-stepping schemes, such as secant and tangent Crank-Nicolson, shifted Crank-Nicolson, and Fractional-Step-Theta, is demonstrated. The numerical experiments are based on a benchmark configuration for fluid-structure interactions.