##
**Flow simulation and high performance computing.**
*(English)*
Zbl 0893.76046

The authors provide a brief review of some advanced high performance computing tools typical of flow simulations of today. A number of three-dimensional simulations are presented, and the examples are illustrated with numerical experiments.

Reviewer: P.K.Mahanti (Ranchi)

### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |

76F10 | Shear flows and turbulence |

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

### Keywords:

three-dimensional simulations
PDF
BibTeX
XML
Cite

\textit{T. Tezduyar} et al., Comput. Mech. 18, No. 6, 397--412 (1996; Zbl 0893.76046)

Full Text:
DOI

### References:

[1] | Ahmed, S.; Ramm, G.; Faltin, G. 1984: Some salient features of the time-averaged ground vehicle wake. SAE Technical Paper Series, 840300 |

[2] | Aliabadi, S.; Ray, S.E.; Tezduyar, T.E. 1993: SUPG finite element computation of compressible flows with the entropy and conservation variables formulations. Computational Mechanics, 11: 300–312 · Zbl 0772.76032 |

[3] | Aliabadi, S.; Tezduyar, T.E. 1993: Space-time finite element computation of compressible flows involving moving boundaries and interfaces. Computer Methods in Applied Mechanics and Engineering, 107 (1–2): 209–224 · Zbl 0798.76037 |

[4] | Aliabadi, S. K.; Tezduyar, T. E. 1995: Parallel fluid dynamics computations in aerospace applications. International Journal for Numerical Methods in Fluids, 21: 783–805 · Zbl 0862.76033 |

[5] | Baker, T. J. 1989: Developments and trends in three-dimensional mesh generation. Applied Numerical Mathematics, 5: 275–304 · Zbl 0675.65120 |

[6] | Barth, T. J. 1992: Aspects of unstructured grids and finite-volume solvers for the Euler and Navier-Stokes equations. In Special Course on Unstructured Grid Methods for Advection Dominated Flows, pages 6-1–6-61. Advisory Group for Aerospace Research and Development |

[7] | Behr, M.; Johnson, A.; Kennedy, J.; Mittal, S.; Tezduyar, T. E. 1993: Computation of incompressible flows with implicit finite element implementations on the Connection Machine. Computer Methods in Applied Mechanics and Engineering, 108: 99–118 · Zbl 0784.76046 |

[8] | Behr, M.; Tezduyar, T. E. 1994: Finite element solution strategies for large-scale flow simulations. Computer Methods in Applied Mechanics and Engineering, 112: 3–24 · Zbl 0846.76041 |

[9] | Bern, M.; Eppstein, D. 1992: Mesh generation and optimal triangulation. Technical report, Xerox Corporation, Palo Alto Research Center · Zbl 0759.68085 |

[10] | Borouchaki, H.; Hecht, F.; Saltel, E.; George, P. L. 1995: Reasonably efficient delaunay based mesh generator in 3 dimensions. In Proceedings 4th International Meshing Roundtable, pages 3–14, Sandia National Laboratories |

[11] | Brooks, A. N.; Hughes, T. J. R. 1982: Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering, 32: 199–259 · Zbl 0497.76041 |

[12] | Cogotti, A. 1983: Aerodynamic characteristics of car wheels. In Technological Advances in Vehicle Design Series, SP3; Impact of Aerodynamics on Vehicle Design, pages 173–196, International Journal of Vehicle Design |

[13] | de Sampaio, P. A. B.; Lyra, P. R. M.; Morgan, K.; Weatherill, N. P. 1993: Petrov-Galerkin solutions of the incompressible Navier-Stokes equations in primitive variables with adaptive remeshing. Computer Methods in Applied Mechanics and Engineering 106: 143–178 · Zbl 0783.76053 |

[14] | Donea, J. 1984: A Taylor-Galerkin method for convective transport problems. International Journal for Numerical Methods in Engineering, 20: 101–120 · Zbl 0524.65071 |

[15] | Farhat, C.; Fezoui, L.; Lanteri, S. 1993: Two-dimensional viscous flow computations on the CM-2: Unstructured meshes, upwind schemes and massively parallel computations. Computer Methods in Applied Mechanics and Engineering, 102: 61–88 · Zbl 0767.76049 |

[16] | Farhat, C.; Lanateri, S. 1994: Simulation of compressible viscous flows on a variety of MPPs: Computational algorithms for unstructured dynamic meshes and performance results. Computer Methods in Applied Mechanics and Engineering, 119: 35–60 · Zbl 0847.76065 |

[17] | Farhat, C.; Lesoinne, M.; Maman, N. 1995: Mixed explicit/implicit time integration of coupled aeroelastic problems: Three-field formulation, geometric conservation and distributed solution. International Journal for Numerical Methods in Fluids, 21: 807–835 · Zbl 0865.76038 |

[18] | Farin, G. 1993: Curves and Surfaces for Computer Aided Geometric Design, A Practical Guide, Academic Press · Zbl 0694.68004 |

[19] | Fortes, A. F. Joseph, D. D.; Lundgren, T. S. 1987: Nonlinear mechanics of fluidization of beds of spherical particles, Journal of Fluid Mechanics, 177: 467–483 |

[20] | Garrard, W. L.; Tezduyar, T. E.; Aliabadi, S. K.; Kalro, V.; Luker, J.; Mittal, S. 1995: Inflation analysis of ram air inflated gliding parachutes. In Proceedings of AIAA 13th Aerodynamic Decelerator Systems Technology, AIAA Paper 95-1565, Clearwater Beach, Florida |

[21] | George, P. L. 1991: Automatic Mesh Generation, Application to Finite Element Methods, John Wiley & Sons · Zbl 0808.65122 |

[22] | Gresho, P.; Chan, S. 1996: Projection 2 goes turbulent-and fully implicit. to appear in International Journal for Numerical Methods in Fluids |

[23] | Hansbo, P. Szepessy, A. 1990: A velocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering, 84: 175–192. · Zbl 0716.76048 |

[24] | Holt, D. J. 1990: Saturn: The vehicles. Automotive Engineering, 98 (11): 34–43 |

[25] | Hu, H. H.; Joseph, D. D.; Crochet, M. J. 1992: Direct simulation of fluid particle motions. Theoretical and Computational Fluid Mechanics, 3: 285–306 · Zbl 0754.76054 |

[26] | Hughes, T. J. R. 1995: Multiscale phenomena: Green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles, and the origins of stabilized methods. Computer Methods in Applied Mechanics and Engineering, 127: 387–401 · Zbl 0866.76044 |

[27] | Hughes, T. J. R.; Brooks, A. N. 1979: A multi-dimensional upwind scheme with no crosswind diffusion. In Hughes, T. J. R., editor, Finite Element Methods for Convection Dominated Flows, AMD-Vol. 34, pages 19–35, ASME, New York |

[28] | Hughes, T. J. R.; Franca, L. P.; Hulbert, G. M. 1989: A new finite element formulation for computational fluid dynamics: VIII. the Galerkin/least-squares method for advective-diffusive equations. Computer Methods in Applied Mechanics and Engineering, 73: 173–189 · Zbl 0697.76100 |

[29] | Hughes, T. J. R.; Franca, L. P.; Mallet, M. 1987: A new finite element formulation for computational fluid dynamics: VI. Convergence analysis of the generalized SUPG formulation for linear time-dependent multi-dimensional advective-diffusive systems. Computer Methods in Applied Mechanics and Engineering 63: 97–112 · Zbl 0635.76066 |

[30] | Hughes, T. J. R.; Hulbert, G. M. 1988: Space-time finite element methods for elasto-dynamics: formulations and error estimates. Computer Methods in Applied Mechanics and Engineering, 66: 339–363 · Zbl 0616.73063 |

[31] | Hughes, T. J. R.; Stewart, J. R. 1996: A space-time formulation for multiscale phenomena. To appear in Journal of Computational and Applied Mathematics · Zbl 0869.65061 |

[32] | Jayaweera, K. O. L. F.; Mason, B. J. 1964: The behavior of clusters of spheres falling in a viscous fluid. Journal of Fluid Mechanics, 20: 121–128 · Zbl 0125.17204 |

[33] | Joe, B. 1991: Construction of three-dimensional Delaunay triangulations using local transformations. Computer Aided Geometric Design, 8: 123–142 · Zbl 0729.65120 |

[34] | Johan, Z.; Hughes, T. J. R.; Mathur, K. K.; Johnsson, S. L. 1992: A data parallel finite element method for computational fluid dynamics on the Connection Machine system. Computer Methods in Applied Mechanics and Engineering, 99 (1): 113–134 · Zbl 0825.76422 |

[35] | Johan, Z.; Hughes, T. J. R.; Shakib, F. 1991: A globally convergent matrix-free algorithm for implicit time-marching schemes arising in finite element analysis in fluids. Computer Methods in Applied Mechanics and Engineering, 87: 281–304 · Zbl 0760.76070 |

[36] | Johan, Z.; Mathur, K. K.; Johnsson, S. L.; Hughes, T. J. R. 1994: An efficient communications strategy for finite element methods on the Connection Machine CM-5 system. Computer Methods in Applied Mechanics and Engineering, 113: 363–387 · Zbl 0846.76046 |

[37] | Johan, Z.; Mathur, K. K.; Johnsson, S. L.; Hughes, T. J. R. 1995: A case study in parallel computation: Viscous flow around an Onera M6 wing. International Journal for Numerical Methods in Fluids, 21: 877–884 · Zbl 0875.76256 |

[38] | Johnson, A. 1995: Mesh Generation and Update Strategies for Parallel Computation of Flow Problems with Moving Boundaries and Interfaces. PhD thesis. University of Minnesota |

[39] | Johnson, A. A.; Tezduyar, T. E. 1994: Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Computer Methods in Applied Mechanics and Engineering, 119: 73–94 · Zbl 0848.76036 |

[40] | Johnson, A. A.; Tezduyar, T. E. 1995: Mesh generation and update strategies for parallel computation of 3D flow problems. In Computational Mechanics, ’95, Proceedings of International Conference on Computational Engineering Science, Mauna Lani, Hawaii · Zbl 0875.76267 |

[41] | Johnson, A. A.; Tezduyar, T. E. 1996a: Parallel computation of incompressible flows with complex geometries. To appear in International Journal for Numerical Methods in Fluids · Zbl 0882.76044 |

[42] | Johnson, A. A.; Tezduyar, T. E. 1996b: Simulation of multiple spheres falling in a liquid-filled tube. To appear in Computer Methods in Applied Mechanics and Engineering · Zbl 0895.76046 |

[43] | Johnson, C.; Navert, U.; Pitkäranta, J. 1984: Finite element methods for linear hyperbolic problems. Computer Methods in Applied Mechanics and Engineering, 45: 285–312 · Zbl 0537.76060 |

[44] | Johnson, C.; Saranen, J. 1986: Streamline diffusion methods for the incompressible Euler and Navier-Stokes equations. Mathematics of Computation, 47: 1–18 · Zbl 0609.76020 |

[45] | Johnsson, S. L.; Mathur, K. K. 1989: Experience with the conjugate gradient method for stress analysis on a data parallel supercomputer. International Journal for Numerical Methods in Engineering, 27: 523–546 |

[46] | Kalro, V.; Aliabadi, S.; Garrard, W.; Tezduyar, T.; Mittal, S.; Stein, K. 1996: Parallel finite element simulation of large ram-air parachutes. To appear in International Journal for Numerical Methods in Fluids · Zbl 0882.76045 |

[47] | Kalro, V.; Tezduyar, T. E. 1995: Parallel finite element computation of 3D incompressible flows on MPPs. In Habashi, W.G., editor, Solution Techniques for Large-Scale CFD Problems, John Wiley & Sons |

[48] | Kashiyama, K.; Ito, H.; Behr, M.; Tezduyar, T. 1995: Three-step explicit finite element computation of shallow water flows on a massively parallel computer. International Journal for Numerical Methods in Fluids, 21: 885–900 · Zbl 0861.76044 |

[49] | Kato, C.; Ikegawa, M. 1991: Large eddy simulation of unsteady turbulent wake of a circular cylinder using the finite element method. In Celik, I., Kobayashi, T.; Ghia, K. N.; Kurokawa, I., editors, Advances in Numerical Simulation of Turbulent Flows, FED-Vol. 117, pages 49–56, New York, ASME |

[50] | Kennedy, J. G.; Behr, M.; Kalro, V.; Tezduyar, T. E. 1994: Implementation of implicit finite element methods for incompressible flows on the CM-5. Computer Methods in Applied Mechanics and Engineering, 119: 95–111 · Zbl 0848.76037 |

[51] | Kobayashi, T. 1992: A review of CFD methods and their application to automobile aerodynamics. In SAE Special Publication SP-908, Vehicle Aerodynamics: Wake Flows, CFD, and Aerodynamic Testing, pages 53–64 |

[52] | Le Beau, G. J.; Ray, S. E.; Aliabadi, S. K.; Tezduyar, T. E. 1993: SUPG finite element computation of compressible flows with the entropy and conservation variables formulations. Computer Methods in Applied Mechanics and Engineering, 104: 397–422 · Zbl 0772.76037 |

[53] | Le Beau, G. J.; Tezduyar, T. E. 1991: Finite element computation of compressible flows with the SUPG formulation. In Dhaubhadel, M. N.; Engelman, M. S.; Reddy, J. N., editors, Advances in Finite Element Analysis in Fluid Dynamics, FED-Vol. 123, pages 21–27, New York, ASME |

[54] | Lingard, J. S. 1995: Ram-air parachute design. In AIAA 13th Aerodynamic Decelerator Conference, 2nd ADS Technology Seminar, Clearwater Beach, Florida |

[55] | Liou, J.; Tezduyar, T. E. 1992: Clustered element-by-element computations for fluid flow. In Simon, H. D., editor, Parallel Computational Fluid Dynamics-Implementation and Results, Scientific and Engineering Computation Series, Chapter 9, pages 167–187, MIT Press, Cambridge, Massachusetts |

[56] | Lynch, D. R. 1982: Unified approach to simulation on deforming elements with application to phase change problems. Journal of Computational Physics, 47 (3): 387–411 · Zbl 0486.65063 |

[57] | Mathur, K. K.; Johnsson, S. L. 1992: Communication primitives for unstructured finite element simulations on data parallel architectures. Computer Systems in Engineering, 3: 63–71 |

[58] | Matsunaga, K.; Miyata, H.; Aoki, K.; Zhu, M. 1992: Finite-difference simulation of 3D vortical flows past road vehicles. In SAE Special Publication SP-908, Vehicle Aerodynamics: Wake Flows, CFD, and Aerodynamic Testing, pages 65–84 |

[59] | Mittal, S.; Tezduyar, T. E. 1994: Massively parallel finite element computation of incompressible flows involving fluid-body interactions. Computer Methods in Applied Mechanics and Engineering, 112: 253–282 · Zbl 0846.76048 |

[60] | Mittal, S.; Tezduyar, T. E. 1995: Parallel finite element simulation of 3d incompressible flows-Fluid-structure interaction. International Journal for Numerical Methods in Fluids, 21: 933–953 · Zbl 0873.76047 |

[61] | Morgan, K.; Peraire, J.; Peiró J. 1992: Unstructured grid methods for compressible flows. In Special Course on Unstructured Grid Methods for Advection Dominated Flows, pages 5-1–5-39. Advisory Group for Aerospace Research and Development |

[62] | Muto, S. 1983: The aerodynamic drag coefficient of a passenger car and methods for reducing it. In Technological Advances in Vehicle Design Series, SP 3; Impact of Aerodynamics on Vehicle Design, pages 57–69, International Journal of Vehicle Design |

[63] | Özturan, C.; deCougny, H. L.; Shephard, M. S.; Flaherty, J. E. 1994: Parallel adaptive mesh refinement and redistribution on distributed memory computers. Computer Methods in Applied Mechanics and Engineering, 119: 123–137 · Zbl 0851.73068 |

[64] | Ray, S. E.; Wren, G. P.; Aliabadi, S. K.; Tezduyar, T. E. 1996: High performance computation of fluid-structure interaction and two-phase flow problems. In Proceedings of the 20th Army Science Conference, Norfolk, Virginia, to appear |

[65] | Saad, Y.; Schultz, M. 1986: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal of Scientific and Statistical Computing, 7: 856–869 · Zbl 0599.65018 |

[66] | Salinger, A. G.; Xiao, Q.; Zhou, Y.; Derby, J. J.; 1994: Massively parallel finite element computations of three-dimensional, time-dependent, incompressible flows in materials processing systems. Computer Methods in Applied Mechanics and Engineering, 119: 139–156 · Zbl 0848.76038 |

[67] | Shakib, F. 1988: Finite Element Analysis of the Compressible Euler and Navier-Stokes Equations. PhD thesis, Department of Mechanical Engineering, Stanford University |

[68] | Shakib, S.; Hughes, T. J. R.; Johan, Z. 1989: A multi-element group preconditioned GMRES algorithm for nonsymmetric systems arising in finite element analysis. Computer Methods in Applied Mechanics and Engineering, 75: 415–456 · Zbl 0687.76065 |

[69] | Shephard, M. S.; Georges, M. K. 1991: Automatic three-dimensional mesh generation by the finite octree technique. International Journal for Numerical Methods in Engineering, 32: 709–749 · Zbl 0755.65116 |

[70] | Smagorinsky, J. 1963: General circulation experiments with the primitive equations. Monthly Weather Review, 91 (3): 99–165 |

[71] | Soulaimani, A.; Fortin, M.; Dhatt, G.; Ouellet, Y. 1991: Finite element simulation of two- and three-dimensional free surface flows. Computer Methods in Applied Mechanics and Engineering, 86: 265–296 · Zbl 0761.76037 |

[72] | Speziale, C. G. 1991: Analytical methods for the development of Reynolds-stress closures in turbulence. Annual Review of Fluid Mechanics, 23: 107–157 · Zbl 0723.76005 |

[73] | Tezduyar, T. E. 1991: Stabilized finite element formulations for incompressible flow computations. Advances in Applied Mechanics, 28: 1–44 · Zbl 0747.76069 |

[74] | Tezduyar, T. E.; Aliabadi, S.; Behr, M.; Johnson, A.; Kalro, V.; Litke, M. 1996: High performance computing techniques for flow simulations. In Papadrakakis, M., editor, Solving Large-Scale Problems in Mechanics: Parallel and Distributed Computer Applications, John Wiley & Sons, to appear · Zbl 0893.76046 |

[75] | Tezduyar, T. E.; Aliabadi, S.; Behr, M.; Johnson, A.; Kalro, V.; Waters, C. 1995: 3D simulation of flow problems with parallel finite element computations on the Cray T3D. In Computational Mechanics ’95, Proceedings of International Conference on Computational Engineering Science, Mauna Lani, Hawaii |

[76] | Tezduyar, T.; Aliabadi, S.; Behr, M.; Johnson, A.; Mittal, S. 1992a: Massively parallel finite element computation of three-dimensional flow problems. In Proceedings of the 6th Japan Numerical Fluid Dynamics Symposium, pages 15–24, Tokyo, Japan |

[77] | Tezduyar, T.; Aliabadi, S.; Behr, M.; Johnson, A.; Mittal, S. 1993: Parallel finite-element computation of 3D flows. IEEE Computer, 26–10 (10): 27–36 · Zbl 0875.76267 |

[78] | Tezduyar, T. E.; Aliabadi, S. K.; Behr, M.; Mittal, S. 1994: Massively parallel finite element simulation of compressible and incompressible flows. Computer Methods in Applied Mechanics and Engineering, 119: 157–177 · Zbl 0848.76040 |

[79] | Tezduyar, T. E.; Behr, M.; Aliabadi, S. K.; Mittal, S.; Ray, S. E. 1992b: A new mixed preconditioning method for finite element computations. Computer Methods in Applied Mechanics and Engineering, 99: 27–42 · Zbl 0762.65060 |

[80] | Tezduyar, T. E.; Behr, M.; Liou, J. 1992c: A new strategy for finite element computations involving moving boundaries and interfaces-the deforming-spatial-domain/space-time procedure: I. The concept and the preliminary tests. Computer Methods in Applied Mechanics and Engineering, 94 (3): 339–351 · Zbl 0745.76044 |

[81] | Tezduyar, T. E.; Behr, M.; Mittal, S.; Johnson, A. A. 1992d: Computation of unsteady incompressible flows with the finite element methods-space-time formulations, iterative strategies and massively parallel implementations. In Smolinski, P.; Liu, W. K.; Hulbert, G.; Tamma, K., editors, New Methods in Transient Analysis, AMD-Vol. 143, pages 7–24, New York, ASME |

[82] | Tezduyar, T. E.; Hughes, T. J. R. 1983: Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations. In Proceedings of AIAA 21st Aerospace Sciences Meeting, AIAA Paper 83-0125, Reno, Nevada |

[83] | Xiao, Q.; Salinger, A. G.; Zhou, Y.; Derby, J. J. 1995: Massively parallel finite element analysis of coupled, incompressible flows: A benchmark computation of baroclinic annulus waves. International Journal for Numerical Methods in Fluids, 21: 1007–1014 · Zbl 0862.76042 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.