Multipoint constraint methods for moving body and non-contiguous mesh simulations†
Corresponding Author
David K. Gartling
Sandia National Laboratories, Engineering Sciences Center, Albuquerque, NM 87185, U.S.A.
Sandia National Laboratories, Engineering Sciences Center, Albuquerque, NM 87185, U.S.A.===Search for more papers by this authorCorresponding Author
David K. Gartling
Sandia National Laboratories, Engineering Sciences Center, Albuquerque, NM 87185, U.S.A.
Sandia National Laboratories, Engineering Sciences Center, Albuquerque, NM 87185, U.S.A.===Search for more papers by this authorThis article is a U.S. Government work and is in the public domain in the U.S.A.
Abstract
A sliding mesh method is demonstrated for moving body simulations involving thermal and fluid problems. Static problems with non-contiguous mesh constructions are also solved using the same methodology. The proposed algorithm employs a parallel implementation of multipoint constraints with an efficient node-in-mesh search procedure. A simple method for treating the problem of partially covered/exposed element surfaces is also summarized. Several examples of static and dynamic thermal conduction and viscous flow problems illustrate the algorithms. Published in 2004 by John Wiley & Sons, Ltd.
REFERENCES
- 1 Tezduyar TE, Behr M, Liou J. A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure. I. The concept and preliminary tests. Computer Methods in Applied Mechanics and Engineering 1992; 94: 339–351.
- 2 Tezduyar TE, Aliabadi S, Behr M. Enhanced-discretization interface-capturing technique. In Proceedings ISAC '97 High Performance Computing on Multiphase Flows, Y Matsumoto, A Prosperetti (eds). Japan Society of Mechanical Engineers, 1997; 1–6.
- 3 Tezduyar TE, Aliabadi S, Behr M. Enhanced-discretization interface-capturing technique (EDICT) for computation of unsteady flows with interfaces. Computer Methods in Applied Mechanics and Engineering 1998; 155: 235–248.
- 4 Tezduyar TE. Finite element methods for flow problems with moving boundaries and interfaces. Archives of Computational Methods in Engineering 2001; 8: 83–130.
- 5 Hughes TJR, Brooks A. A multi-dimensional upwind scheme with no crosswind diffusion. In Finite Element Methods for Convection Dominated Flows, TJR Hughes (ed.), vol. AMD-34. ASME: New York, 1979; 19–35.
- 6 Tezduyar TE. Stabilized finite element formulations for incompressible flow computations. Advances in Applied Mechanics 1991; 28: 1–44.
- 7 Hirt CW, Nicholls BD. Volume of fluid (VOF) method for dynamics of free boundaries. Journal of Computational Physics 1981; 39: 201–225.
- 8 Sethian JA. Level Set Methods and Fast Marching Methods. Cambridge University Press: Cambridge, UK, 1999.
- 9 Lynch DR. Unified approach to simulation on deforming elements with application to phase change problems. Journal of Computational Physics 1982; 47: 387–411.
- 10 Cairncross RA, Schunk PR, Baer TA, Rao RR, Sackinger PA. A finite element method for free surface flows of incompressible fluids in three dimensions, Part I. Boundary fitted mesh motion. International Journal for Numerical Methods in Fluids 2000; 33: 375–403.
- 11 Löhner R, Yang C, Baum JD, Luo H, Pelessone D, Charman C. The numerical simulation of strongly unsteady flows with hundreds of moving bodies. International Journal for Numerical Methods in Fluids 1999; 31: 113–120.
- 12 Cruchaga M, Celentano D, Tezduyar T. A moving Lagrangian interface technique for flow computation over fixed meshes. Computer Methods in Applied Mechanics and Engineering 2001; 191: 525–543.
- 13 Peskin CS, McQueen DM. A three-dimensional computational method for blood flow in the heart: I. Immersed elastic fibers in a viscous incompressible fluid. Journal of Computational Physics 1989; 81: 372–405.
- 14 Peskin CS. The immersed boundary method. Acta Numerica 2002; 11: 479–517.
10.1017/S0962492902000077 Google Scholar
- 15 Zhang L, Gerstenberger A, Wang X, Liu WK. Immersed finite element method. Computer Methods in Applied Mechanics and Engineering 2004, in press.
- 16 Glowinski R, Pan T, Periaux J. A fictitious domain method for Dirichlet problem and application. Computer Methods in Applied Mechanics and Engineering 1994; 111: 283–303.
- 17 Bertrand F, Tanguy PA, Thibault F. A three-dimensional fictitious domain method for incompressible fluid flow problems. International Journal for Numerical Methods in Fluids 1997; 25: 719–736.
- 18 Bernardi C, Maday Y, Patera AT. A new nonconforming approach to domain decomposition: the mortar element method. In Nonlinear Partial Differential Equations and Their Applications, H Brezis, J-L Lions (eds). Longman Scientific & Technical: Harlow, UK, 1994; 13–51.
10.1007/BFb0073871 Google Scholar
- 19 Gropp W, Lusk E, Skjellum A. Using MPI. MIT Press: Cambridge, MA, 1995.
- 20 Buffa A, Maday Y, Rapetti F. Calculation of eddy currents in moving structures by a sliding mesh-finite element method. IEEE Transactions on Magnetics 2000; 36: 1356–1359.
- 21 Tezduyar TE, Aliabadi S, Behr M, Johnson A, Kalro V, Litke M. Flow simulation and high performance computing. Computational Mechanics 1996; 18: 397–412.
- 22 Behr M, Tezduyar TE. Shear-slip mesh update method. Computer Methods in Applied Mechanics and Engineering 1999; 174: 261–274.
- 23 Plimpton S, Hendrickson B, Stewart J. A parallel rendezvous algorithm for interpolation between multiple grids. Proceedings of ACM/IEEE SuperComputing98 Conference, Orlando, FL, 1998.
- 24 Berger MJ, Bokhari SH. A partitioning strategy for nonuniform problems on multiprocessors. IEEE Transactions on Computers 1987; 36: 570–580.
- 25 Rashid M. The arbitrary local mesh replacement method: an alternative to remeshing for crack propagation analysis. Computer Methods in Applied Mechanics and Engineering 1998; 154: 133–150.
- 26 Clay RL, Mish KD, Otero IJ, Taylor LM, Williams AB. An annotated reference guide to the finite element interface (FEI) specification, Version 1.0. Sandia Report SAND99-8229, Sandia National Laboratories, Albuquerque, NM, 1999.
- 27 Gartling DK, Hogan RE, Glass MW. COYOTE—A finite element computer program for nonlinear heat conduction problems. Sandia Report SAND94-1173, SAND94-1179, Sandia National Laboratories, Albuquerque, NM, 2003.
- 28 Gartling DK. KACHINA—A finite element computer program for viscous, incompressible flow problems. Sandia Report, Sandia National Laboratories, Albuquerque, NM, 2004, in preparation.
- 29 Gartling DK. TORO—A finite element computer program for nonlinear quasi-static problems in elctromagnetics. Sandia Report SAND95-2472, SAND96-0903, Sandia National Laboratories, Albuquerque, NM, 2003.
- 30 Gresho PM, Lee RL, Chan S, Sani RL. Solution of the time-dependent, incompressible Navier–Stokes and Boussinesq equations using the Galerkin finite element method. Proceedings of IUTAM Symposium on Approximation Methods for Navier–Stokes Problems, Paderborn, Germany, 1979.
Citing Literature
Special Issue on Advances and Challenges in Flow Simulation and Modelling
28 February ‐ 10 March 2005
Pages 471-489