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

T. Wick ()
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T. Wick: University of Heidelberg, Institute of Applied Mathematics

A chapter in Numerical Mathematics and Advanced Applications 2011, 2013, pp 625-632 from Springer

Abstract: 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.

Keywords: Temporal Discretization; Kirchhoff Material; Inflow Velocity Profile; Venant Kirchhoff Material; Galerkin Finite Element Scheme (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-33134-3_66

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DOI: 10.1007/978-3-642-33134-3_66

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