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

International Journal for Numerical Methods in Engineering

Volumn 84, Issue 1, 2010, Pages 73-107

  Farhat, C ^a,b   Rallu, A ^b   Wang, K ^b   Belytschko, T ^c  

^a Department of Aeronautics and Astronautics Department of Mechanical Engineering and Industrial for Computational and Mathematical Engineering   (United States)

^b Stanford University   (United States)

^c Northwestern University   (United States)

Author keywords

Added mass; Implosion; Loosely coupled; Non linear fluid structure; Second order time accurate; Staggered time integrator

Indexed keywords

ADDED MASS; IMPLOSION; LOOSELY COUPLED; NON-LINEAR; SECOND ORDERS; STAGGERED TIME-INTEGRATOR;

FLUID STRUCTURE INTERACTION; INTEGRATION; RUNGE KUTTA METHODS; TRANSONIC FLOW;

FLUIDS;

EID: 77956937549     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2883     Document Type: Article

References (41)

1. Park KC, Felippa CA, DeRuntz JA. Stabilization of staggered solution procedures for fluid-structure interaction analysis. In Computational Methods for Fluid-Structure Interaction Problems, Belytshcko T, Geers T (eds). ASME Applied Mechanics Symposia Series, vol. 26. AMD: New York, 1977; 94-124.
2. Piperno S, Farhat C, Larrouturou B. Partitioned procedures for the transient solution of coupled aeroelastic problems-Part I: model problem, theory, and two-dimensional application. Computer Methods in Applied Mechanics and Engineering 1995; 124:79-112.
3. Morton SA, Melville RB, Visbal MR. Accuracy and coupling issues of aeroelastic Navier-Sokes solutions of deforming meshes. AIAA Paper 97-1085, 38th AIAA Structures, Structural Dynamics and Materials Conference, Kissimmee, Florida, 7-10 April 1997.
4. Farhat C, Lesoinne M. Two efficient staggered procedures for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems. Computer Methods in Applied Mechanics and Engineering 2000; 182:499-516.
5. Le Tallec P, Mouro J. Fluid structure interaction with large structural displacements. Computer Methods in Applied Mechanics and Engineering 2001; 190:3039-3068.
6. Piperno S, Farhat C. Partitioned procedures for the transient solution of coupled aeroelastic problems-Part II: energy transfer analysis and three-dimensional applications. Computer Methods in Applied Mechanics and Engineering 2001; 190:3147-3170.
7. Causin P, Gerbeau JF, Nobile F. Added-mass effect in the design of partitioned algorithms for fluid-structure problems. Computer Methods in Applied Mechanics and Engineering 2005; 194:4506-4527.
8. Farhat C, van der Zee KG, Geuzaine P. Provably second-order time-accurate loosely coupled solution algorithms for transient nonlinear computational aeroelasticity. Computer Methods in Applied Mechanics and Engineering 2006; 195:1973-2001.
9. Zilian A, Legay A. The enriched space-time finite element method (EST) for simultaneous solution of fluid-structure interaction. International Journal for Numerical Methods in Engineering 2008; 75:305-334.
10. Ishihara D, Yoshimura S. A monolithic approach for interaction of incompressible viscous fluid and an elastic body based on fluid pressure Poisson equation. International Journal for Numerical Methods in Engineering 2005; 64:167-203.
11. Hubner B, Dinkler D. A simultaneous solution procedure for strong interactions of generalized Newtonian fluids and viscoelastic solids at large strains. International Journal for Numerical Methods in Engineering 2005; 64:920-939.
12. Rochus V, Rixen DJ, Golinval J-C. Monolithic modelling of electro-mechanical coupling in micro-structures. International Journal for Numerical Methods in Engineering 2006; 65:461-493.
13. Pramono E, Weeratunga SK. Aeroelastic computations for wings through direct coupling on distributed-memory MIMD parallel computers. AIAA Paper No. 94-0095, 32nd Aerospace Sciences Meeting & Exhibit, Reno, 10-13 January 1994.
14. Farhat C, Lesoinne M, Maman N. Mixed explicit/implicit time integration of coupled aeroelastic problems: three-field formulation, geometric conservation and distributed solution. International Journal for Numerical Methods in Fluids 1995; 21:807-835.
15. Belytschko T, Kennedy JM. Computer-models for subassembly simulation. Nuclear Engineering and Design 1978; 49:17-38.
16. Donea J, Giuliani S, Halleux JP. An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-Structure interactions. Computer Methods in Applied Mechanics and Engineering 1982; 33:689-723.
17. Farhat C, Rallu A, Shankaran S. A higher-order generalized ghost fluid method for the poor for the threedimensional two-phase flow computation of underwater implosions. Journal of Computational Physics 2008; 227:7674-7700.
18. Geuzaine P, Grandmont C, Farhat C. Design and analysis of ALE schemes with provable second-order timeaccuracy for inviscid and viscous flow simulations. Journal of Computational Physics 2003; 191:206-227.
19. Farhat C, Geuzaine P. Design and analysis of robust ALE time-integrators for the solution of unsteady flow problems on moving grids. Computer Methods in Applied Mechanics and Engineering 2004; 193:4073-4095.
20. Roe PL. Approximate Riemann solvers, parameter vectors and difference schemes. Journal of Computational Physics 1981; 43:357-372.
21. Rausch RD, Batina JT, Yang TY. Euler flutter analysis of airfoils using unstructured dynamic meshes. AIAA Paper No. 89-13834, 30th Structures, Structural Dynamics and Materials Conference, Mobile, Alabama, 3-5 April 1989.
22. Farhat C, Degand C, Koobus B, Lesoinne M. Torsional springs for two-dimensional dynamic unstructured fluid meshes. Computer Methods in Applied Mechanics and Engineering 1998; 163:231-245.
23. Degand C, Farhat C. A three-dimensional torsional spring analogy method for unstructured dynamic meshes. Computers and Structures 2002; 80:305-316.
24. Cebral JR, Lohner R. Conservative load projection and tracking for fluid-structure problems. AIAA Journal, 1997; 35:687-692.
25. Farhat C, Lesoinne M, LeTallec P. Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: momentum and energy conservation, optimal discretization and application to aeroelasticity. Computer Methods in Applied Mechanics and Engineering 1998; 157:95-114.
26. Lesoinne M, Sarkis M, Hetmaniuk U, Farhat C. A linearized method for the frequency analysis of threedimensional fluid/structure interaction problems in all flow regimes. Computer Methods in Applied Mechanics and Engineering 2001; 190:3121-3146.
27. Lieu T, Farhat C, Lesoinne M. Reduced-order fluid/structure modeling of a complete aircraft configuration. Computer Methods in Applied Mechanics and Engineering 2006; 195:5730-5742.
28. Amsallem D, Farhat C. An interpolation method for adapting reduced-order models and application to aeroelasticity. AIAA Journal 2008; 46:1803-1813.
29. Geuzaine P, Brown G, Harris C, Farhat C. Aeroelastic dynamic analysis of a full F-16 configuration for various flight conditions. AIAA Journal 2003; 41:363-371.
30. Farhat C, Geuzaine P, Brown G. Application of a three-field nonlinear fluid-structure formulation to the prediction of the aeroelastic parameters of an F-16 fighter. Computers and Fluids 2003; 32:3-29.
31. Farhat C, Rajasekharan A, Koobus B. A dynamic variational multiscale method for large eddy simulations on unstructured meshes. Computer Methods in Applied Mechanics and Engineering 2006; 195:1667-1691.
32. Turkel E. Preconditioning techniques in computational fluid dynamics. Annual Reviews in Fluid Mechanics 1999; 31:385-416.
33. Roe PL. Approximate Riemann solvers, parameter vectors and difference schemes. Journal of Computational Physics 1981; 43:357-372.
34. van Leer B. Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method. Journal of Computational Physics 1979; 32:101-136.
35. Saad Y, Schultz MH. GMRES a generalized minimal residual algorithm for solving nonsymmetric linear problems. SIAM Journal on Scientific and Statistical Computing 1986; 7(3):856-869.
36. Cai XC, Farhat C, Sarkis M. A minimum overlap restricted additive Schwarz preconditioner and applications in 3D flow simulations. Contemporary Mathematics 1998; 218:478-484.
37. Lesoinne M, Lieu T. A geometrically non-linear mesh motion technique for large displacements of unstructured fluid meshes for aeroelastic simulations. Proceedings of the European Conference on Computational Mechanics (ECCM), Cracow, Poland, 26-29 June 2001.
38. Maman N, Farhat C. Matching fluid and structure meshes for aeroelastic computations: a parallel approach. Computers and Structures 1995; 54(4):779-785.
39. Belytschko T, O Neal M. Contact-impact by the pinball algorithm with penalty and Lagrangian-methods. International Journal for Numerical Methods in Engineering 1991; 3:547-572.
40. Petzold L. Differential/algebraic equations are not ODE's. SIAM Journal on Scientific and Statistical Computing 1982; 3:367-384.
41. Farhat C, Crivelli L, Géeradin M. Implicit time integration of a class of constrained hybrid formulations-Part I: spectral stability theory. Computer Methods in Applied Mechanics and Engineering 1995; 125:71-107.