A higher-order time integration algorithm for the simulation of nonlinear fluid–structure interaction

Abstract In this paper higher-order time integration schemes are applied to nonlinear fluid–structure interaction (FSI) simulations. For a given accuracy, we investigate the efficiency of higher-order time integration schemes compared to lower-order methods. In the partitioned FSI simulations on a one-dimensional piston problem, a mixed implicit/explicit (IMEX) time integration scheme is employed: the implicit scheme is used to integrate the fluid and structural dynamics, whereas an explicit Runge–Kutta scheme integrates the coupling terms. The resulting IMEX scheme retains the order of the implicit and explicit schemes. In the IMEX scheme considered, the implicit scheme consists of an explicit first stage, singly diagonally implicit Runge–Kutta (ESDIRK) scheme, which is a multi-stage, L-stable scheme.

[1]  Ernst Hairer,et al.  Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .

[2]  C. Farhat,et al.  Partitioned procedures for the transient solution of coupled aroelastic problems Part I: Model problem, theory and two-dimensional application , 1995 .

[3]  M. Carpenter,et al.  Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations , 2003 .

[4]  C. Farhat,et al.  Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems , 2000 .

[5]  Charbel Farhat,et al.  On the significance of the geometric conservation law for flow computations on moving meshes , 2000 .

[6]  C. Hirsch,et al.  Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.

[7]  Charbel Farhat,et al.  Aeroelastic Dynamic Analysis of a Full F-16 Configuration for Various Flight Conditions , 2003 .

[8]  Charbel Farhat,et al.  Partitioned procedures for the transient solution of coupled aeroelastic problems , 2001 .

[9]  Hester Bijl,et al.  Implicit Time Integration Schemes for the Unsteady Compressible Navier–Stokes Equations: Laminar Flow , 2002 .

[10]  Lorenzo Pareschi,et al.  A Numerical Method for the Accurate Solution of the Fokker–Planck–Landau Equation in the Nonhomogeneous Case , 2002 .

[11]  Frederic Blom,et al.  A monolithical fluid-structure interaction algorithm applied to the piston problem , 1998 .

[12]  H. Bijl,et al.  Application of Higher Order Runge-Kutta Time Integrators in Partitioned Fluid-Structure Interaction Simulations , 2003 .

[13]  Charbel Farhat,et al.  The discrete geometric conservation law and the nonlinear stability of ALE schemes for the solution of flow problems on moving grids , 2001 .

[14]  Haym Benaroya,et al.  IUTAM Symposium on Integrated Modeling of Fully Coupled Fluid Structure Interactions Using Analysis, Computations, and Experiments : proceedings of the IUTAM Symposium held at Rutgers University, New Jersey, U.S.A., 2-6 June 2003 , 2003 .