Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity Charbel Farhat a, * , Kristoffer G. van der Zee b,1 , Philippe Geuzaine c,2 a Department of Mechanical Engineering and Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305-3035, USA b Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands c CENAERO, Ba ˆtiment Mermoz 1, Avenue Jean Mermoz, 30, B-6041 Gosselies, Belgium Received 1 April 2004; received in revised form 1 November 2004; accepted 3 November 2004 Abstract A methodology for designing formally second-order time-accurate and yet loosely-coupled partitioned procedures for the solution of nonlinear fluid–structure interaction (FSI) problems on moving grids is presented. Its key compo- nents are a fluid time-integrator that is provably second-order time-accurate on moving grids, the midpoint rule for advancing in time the solution of the structural dynamics equations of motion, a second-order structure predictor for bypassing the inner-iterations encountered in strongly-coupled solution procedures, and a carefully designed algo- rithm for time-integrating the motion of the fluid-mesh. Following this methodology, two different loosely-coupled schemes are constructed for the solution of transient nonlinear FSI problems and proved to be second-order time-accu- rate. Three-dimensional numerical results pertaining to the simulation of the aeroelastic response to a gravity excitation of a complete F-16 configuration are also presented. In addition to confirming the theoretical results discussed in this paper, these numerical results highlight a very stable behavior of the designed loosely-coupled partitioned procedures. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Aeroelasticity; Fluid–structure interaction; Loosely-coupled algorithm; Partitioned procedure; Second-order time-accuracy 0045-7825/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cma.2004.11.031 * Corresponding author. Tel.: +1 650 723 3840; fax: +1 650 725 3525. E-mail address: cfarhat@stanford.edu (C. Farhat). 1 This work was done while the author was visiting the University of Colorado at Boulder. 2 This work was done while the author was employed at the University of Colorado at Boulder. Comput. Methods Appl. Mech. Engrg. 195 (2006) 1973–2001 www.elsevier.com/locate/cma