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Massively parallel finite element simulation of compressible and incompressible flows. (English) Zbl 0848.76040

We present a review of where our research group stands in parallel finite element simulation of flow problems on the Connection Machines, an effort that started for our group in the fourth quarter of 1991. This review includes an overview of our work on computation of flow problems involving moving boundaries and interfaces, such as free surfaces, two-liquid interfaces, and fluid-structure and fluid-particle interactions. With numerous examples, we demonstrate that, with these new computational capabilities, today we are at a point where we routinely solve practical flow problems, including those in three dimensions and those involving moving boundaries and interfaces.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
65Y05 Parallel numerical computation
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[1] Tezduyar, T. E.; 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 the preliminary tests, Comput. Methods Appl. Mech. Engrg., 94, 339-351 (1992) · Zbl 0745.76044
[2] Tezduyar, T. E.; Behr, M.; Mittal, S.; Liou, J., A new strategy for finite element computations involving moving boundaries and interfaces — the deforming-spatial-domain/space-time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders, Comput. Methods Appl. Mech. Engrg., 94, 353-371 (1992) · Zbl 0745.76045
[3] Tezduyar, T. E.; Hughes, T. J.R., Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations, (Proc. AIAA 21st Aerospace Sciences Meeting. Proc. AIAA 21st Aerospace Sciences Meeting, Reno, Nevada. Proc. AIAA 21st Aerospace Sciences Meeting. Proc. AIAA 21st Aerospace Sciences Meeting, Reno, Nevada, AIAA Paper 83-0125 (1983)) · Zbl 0535.76074
[4] Le Beau, G. J.; Tezduyar, T. E., Finite element computation of compressible flows with the SUPG formulation, (Dhaubhadel, M. N.; Engelman, M. S.; Reddy, J. N., Advances in Finite Element Analysis in Fluid Dynamics, FED, Vol. 123 (1991), ASME: ASME New York), 21-27
[5] Aliabadi, S.; Ray, S. E.; Tezduyar, T. E., SUPG finite element computation of compressible flows with the entropy and conservation variables formulations, Comput. Mech., 11, 300-312 (1993) · Zbl 0772.76032
[6] Hughes, T. J.R.; Franca, L. P.; Hulbert, G. M., A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations, Comput. Methods Appl. Mech. Engrg., 73, 173-189 (1989) · Zbl 0697.76100
[7] Hansbo, P.; Szepessy, A., A velocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 84, 175-192 (1990) · Zbl 0716.76048
[8] Hughes, T. J.R.; Franca, L. P.; Mallet, M., 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, Comput. Methods Appl. Mech. Engrg., 63, 97-112 (1987) · Zbl 0635.76066
[9] Shakib, F., Finite element analysis of the compréssible Euler and Navier-Stokes equations, (Ph.D. Thesis (1988), Department of Mechanical Engineering, Stanford University)
[10] Hughes, T. J.R.; Hulbert, G. M., Space-time finite element methods for elastodynamics: formulations and error estimates, Comput. Methods Appl. Mech. Engrg., 66, 339-363 (1988) · Zbl 0616.73063
[11] Tezduyar, T. E., Stabilized finite element formulations for incompressible flow computations, Adv. Appl. Mech., 28, 1-44 (1991) · Zbl 0747.76069
[12] Tezduyar, T. E.; Mittal, S.; Ray, S. E.; Shih, R., Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements, Comput. Methods Appl. Mech. Engrg., 95, 221-242 (1992) · Zbl 0756.76048
[13] Aliabadi, S.; Tezduyar, T. E., Space-time finite element computation of compressible flows involving moving boundaries and interfaces, Comput. Methods Appl. Mech. Engrg., 107, 209-224 (1993) · Zbl 0798.76037
[14] Aliabadi, S.; Tezduyar, T. E., Massively parallel compressible flow computations in aerospace applications, (Extended Abstracts of the Second Japan-US Symposium on Finite Element Methods in Large-Scale Computational Fluid Dynamics. Extended Abstracts of the Second Japan-US Symposium on Finite Element Methods in Large-Scale Computational Fluid Dynamics, Tokyo, Japan (1994)) · Zbl 0862.76033
[16] Mittal, S.; Ratner, A.; Hastreiter, D.; Tezduyer, T. E., Space-time finite element computation of incompressible flows with emphasis on flows involving oscillating cylinders, Internat. Video J. of Engrg. Res., 1, 83-96 (1991)
[17] Mittal, S.; Tezduyar, T. E., A finite element study of incompressible flows past oscillating cylinders and airfoils, Internat. J. Numer. Methods Fluids, 15, 1073-1118 (1992)
[18] Tezduyar, T. E.; Behr, M.; Mittal, S.; Johnson, A. A., Computation of unsteady incompressible flows with the finite element methods — space-time formulations, iterative strategies and massively parallel implementations, (Smolinski, P.; Liu, W. K.; Hulbert, G.; Tamma, K., New Methods in Transient Analysis, AMD, Vol. 143 (1992), ASME: ASME New York), 7-24
[19] Behr, M.; Johnson, A.; Kennedy, J.; Mittal, S.; Tezduyar, T. E., Computation of incompressible flows with implicit finite element implementations on the Connection Machine, Comput. Methods Appl. Mech. Engrg., 108, 99-118 (1993) · Zbl 0784.76046
[20] Mittal, S.; Tezduyar, T. E., Massively parallel finite element computation of incompressible flows involving fluid-body interactions, Comput. Methods Appl. Mech. Engrg., 112, 253-282 (1994) · Zbl 0846.76048
[21] Mittal, S.; Tezduyar, T. E., Massively parallel finite element simulation of incompressible flows, (Extended Abstracts of the Second Japan-US Symposium on Finite Element Methods in Large-Scale Computational Fluid Dynamics. Extended Abstracts of the Second Japan-US Symposium on Finite Element Methods in Large-Scale Computational Fluid Dynamics, Tokyo, Japan (1994)) · Zbl 0846.76048
[23] Tezduyar, T.; Aliabadi, S.; Behr, M.; Johnson, A.; Mittal, S., Massively parallel finite element computation of three-dimensional flow problems, (Proc. 6th Japan Numerical Fluid Dynamics Symposium. Proc. 6th Japan Numerical Fluid Dynamics Symposium, Tokyo, Japan (1992)), 15-24
[24] Tezduyar, T.; Aliabadi, S.; Behr, M.; Johnson, A.; Mittal, S., Parallel finite-element computation of 3D flows, IEEE Comput., 26, 10, 27-36 (1993)
[25] Johnson, A. A.; Tezduyar, T. E., Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces, Comput. Methods Appl. Mech. Engrg., 119, 73 (1994) · Zbl 0848.76036
[26] Lynch, D. R., Unified approach to simulation on deforming elements with application to phase change problems, J. Comput. Phys., 47, 387-411 (1982) · Zbl 0486.65063
[27] Behr, M.; Tezduyar, T. E., Finite element solution strategies for large-scale flow simulations, Comp. Methods Appl. Mech. Engrg., 112, 3-24 (1994) · Zbl 0846.76041
[28] Kennedy, J. G.; Kalro, V.; Behr, M.; Tezduyar, T. E., A strategy for implementing implicit finite element methods for incompressible fluids on the CM-5, (Extended Abstracts of the Second Japan-US Symposium on Finite Element Methods in Large-Scale Computational Fluid Dynamics. Extended Abstracts of the Second Japan-US Symposium on Finite Element Methods in Large-Scale Computational Fluid Dynamics, Tokyo, Japan (1994)) · Zbl 0848.76037
[29] Kennedy, J. G.; Behr, M.; Kalro, V.; Tezduyar, T. E., Implementation of implicit finite element methods for incompressible flows on the CM-5, Comput. Methods Appl. Mech. Engrg., 119, 95 (1994) · Zbl 0848.76037
[30] Saad, Y.; Schultz, M., GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Scientific and Statistical Comput., 7, 856-869 (1986) · Zbl 0599.65018
[31] Coles, D., Transition in circular Couette flow, J. Fluid Mech., 21, 385-425 (1965) · Zbl 0134.21705
[32] Feng, Z. C.; Sethna, P. R., Symmetry-breaking bifurcations in resonant surface waves, J. Fluid Mech., 199, 495-518 (1989) · Zbl 0659.76026
[33] Kato, C.; Ikegawa, M., Large eddy simulation of unsteady turbulent wake of a circular cylinder using the finite element method, (Celik, I.; Kobayashi, T.; Ghia, K. N.; Kurokawa, J., Advances in Numerical Simulation of Turbulent Flows, FED, Vol. 117 (1991), ASME: ASME New York), 49-56
[34] Paidoussis, M. P.; Issid, N. T., Dynamic stability of pipes conveying fluid, J. Sound and Vibration, 33, 267-294 (1974)
[35] Schlichting, H., Boundary-Layer Theory (1979), McGraw-Hill: McGraw-Hill New York
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.