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Stability Estimates and Numerical Comparison of Second Order Time-Stepping Schemes for Fluid-Structure Interactions

In: Numerical Mathematics and Advanced Applications 2011

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  • T. Wick

    (University of Heidelberg, Institute of Applied Mathematics)

Abstract

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.

Suggested Citation

  • T. Wick, 2013. "Stability Estimates and Numerical Comparison of Second Order Time-Stepping Schemes for Fluid-Structure Interactions," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 625-632, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_66
    DOI: 10.1007/978-3-642-33134-3_66
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