Robust and provably second-order explicit–explicit and implicit–explicit staggered time-integrators for highly non-linear compressible fluid–structure interaction problems

Authors

  • C. Farhat,

    Corresponding author
    1. Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, U.S.A.
    2. Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, U.S.A.
    3. Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, U.S.A.
    • Department of Aeronautics and Astronautics, Stanford University, 496 Lomita Mall, Stanford, CA 94305, U.S.A.
    Search for more papers by this author
  • A. Rallu,

    1. Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, U.S.A.
    Search for more papers by this author
  • K. Wang,

    1. Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, U.S.A.
    Search for more papers by this author
  • T. Belytschko

    1. Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, U.S.A.
    Search for more papers by this author

Abstract

An explicit–explicit staggered time-integration algorithm and an implicit–explicit counterpart are presented for the solution of non-linear transient fluid–structure interaction problems in the Arbitrary Lagrangian–Eulerian (ALE) setting. In the explicit–explicit case where the usually desirable simultaneous updating of the fluid and structural states is both natural and trivial, staggering is shown to improve numerical stability. Using rigorous ALE extensions of the two-stage explicit Runge–Kutta and three-point backward difference methods for the fluid, and in both cases the explicit central difference scheme for the structure, second-order time-accuracy is achieved for the coupled explicit–explicit and implicit–explicit fluid–structure time-integration methods, respectively, via suitable predictors and careful stagings of the computational steps. The robustness of both methods and their proven second-order time-accuracy are verified for sample application problems. Their potential for the solution of highly non-linear fluid–structure interaction problems is demonstrated and validated with the simulation of the dynamic collapse of a cylindrical shell submerged in water. The obtained numerical results demonstrate that, even for fluid–structure applications with strong added mass effects, a carefully designed staggered and subiteration-free time-integrator can achieve numerical stability and robustness with respect to the slenderness of the structure, as long as the fluid is justifiably modeled as a compressible medium. Copyright © 2010 John Wiley & Sons, Ltd.

Ancillary