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Computation of incompressible flows with implicit finite element implementations on the Connection Machine. (English) Zbl 0784.76046

Two implicit finite element formulations for incompressible flows have been implemented on the Connection Machine supercomputers and successfully applied to a set of time-dependent problems. The stabilized space-time formulation for moving boundaries and interfaces, and a new stabilized velocity-pressure-stress formulation are both described, and significant aspects of the implementation of these methods on massively parallel architectures are discussed. Several numerical results for flow problems involving moving as well as fixed cylinders and airfoils are reported.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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[1] Belytschko, T.; Plaskacz, E. J.; Kennedy, J. M.; Greenwell, D. L., Finite element analysis on the CONNECTION machine, Comput. Methods Appl. Mech. Engrg., 81, 229-254 (1990) · Zbl 0728.73068
[2] Farhat, C.; Fezoui, L.; Lanteri, S., Mixed finite volume / finite element massively parallel computations: Euler flows, unstructured grids, and upwind computations, (Mehrotra, P.; Saltz, J.; Voigt, R., Unstructured Scientific Computation on Scalable Multiprocessors (1992), MIT Press: MIT Press Cambridge, MA), 253-283
[3] Johnsson, S. L.; Mathur, K. K., Experience with the conjugate gradient method for stress analysis on a data parallel supercomputer, Internat. J. Numer. Methods Engrg., 27, 523-546 (1989)
[4] Johnsson, S. L.; Mathur, K. K., Data structures and algorithms for the finite element method on a data parallel supercomputer, Internat. J. Numer. Methods Engrg., 29, 881-908 (1990) · Zbl 0729.73239
[5] Mathur, K. K.; Johnsson, S. L., The finite element method on a data parallel computing system, Internat. J. High Speed Comput., 1, 29-44 (1989) · Zbl 0725.73088
[6] Mathur, K. K., On the use of randomized address maps in unstructured three-dimensional finite element simulations, (Technical Report TMC-37 / CS90-4 (1990), Thinking Machines Machines Corporation: Thinking Machines Machines Corporation 245 First Street, Cambridge, MA 02142)
[7] Johan, Z.; Hughes, T. J.R.; Mathur, K. K.; Johnsson, S. L., A data parallel finite element method for computational fluid dynamics on the Connection Machine system, Comput. Methods Appl. Mech. Engrg., 99, 113-134 (1992) · Zbl 0825.76422
[8] Farhat, C., On the mapping of massively parallel processors onto finite element graphs, Comput. & Structures, 32, 347-354 (1989) · Zbl 0711.73225
[9] 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 numerical tests, Comput. Methods Appl. Mech. Engrg., 94, 339-351 (1992) · Zbl 0745.76044
[10] 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
[11] 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)
[12] Behr, M. A.; Franca, L. P.; Tezduyar, T. E., Stabilized finite element methods for the velocity-pressure-stress formulation of incompressible flows, Comput. Methods Appl. Mech. Engrg., 104, 31-48 (1993) · Zbl 0771.76033
[13] Thinking Machines Corporation, (CM Fortran Programming Guide (1991)), 245 First Street, Cambridge, MA 02142
[14] Lohner, R.; Camberos, J.; Merriam, M., Parallel unstructured grid generation, (Proc. 10th Computational Fluid Dynamics Conf.. Proc. 10th Computational Fluid Dynamics Conf., Honolulu, Hawaii. Proc. 10th Computational Fluid Dynamics Conf.. Proc. 10th Computational Fluid Dynamics Conf., Honolulu, Hawaii, AIAA Paper 91-1582-CP (1991)) · Zbl 0825.76680
[15] Dannenhoffer, J. F.; Haimes, R.; Giles, M. B., Data compression through the use of grid adaptation techniques, (Proc. 10th Computational Fluid Dynamics Conf.. Proc. 10th Computational Fluid Dynamics Conf., Honolulu, Hawaii (1991)), 983-984
[16] Cormen, T. H.; Leiserson, C. E.; Rivest, R. L., Introduction to Algorithms (1990), McGraw-Hill: McGraw-Hill New York · Zbl 1158.68538
[17] Pothen, A.; Simon, H. D.; Liou, K. P., Partitioning sparse matrices with eigenvectors of graphs, SIAM J. Matrix Anal. Applic., 11, 430-452 (1990) · Zbl 0711.65034
[18] Schreiber, R.; Hammond, S., Mapping unstructured grid problems to the Connection Machine, (RIACS Technical Report TR90.22 (1990), NASA Ames Research Center: NASA Ames Research Center Moffett Field, CA 94035)
[19] Pothen, A.; Simon, H. D.; Wang, L., Spectral nested dissection, (Technical Report RNR-92-003 (1992), NASA Ames Research Center: NASA Ames Research Center Moffett Field, CA 94035)
[20] Johan, Z., Data parallel finite element techniques for large-scale computational fluid dynamics, (Ph.D. Thesis (1992), Stanford University)
[21] Saad, Y.; Schultz, M., GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 7, 856-869 (1986) · Zbl 0599.65018
[23] Hughes, T. J.R., The Finite Element Method, (Linear Static and Dynamic Finite Element Analysis (1987), Prentice Hall: Prentice Hall Englewood Cliffs, NJ) · Zbl 0535.76074
[24] Thinking Machines Corporation, (CMSSL Release Notes — Version 2.2 (1991)), 245 First Street, Cambridge, MA 02142
[25] Tuncer, I. H.; Wu, J. C.; Wang, C. M., Theoretical and numerical studies of oscillating airfoils, AIAA J., 28, 1615-1624 (1990)
[26] Ohmi, K.; Coutanceau, M.; Daube, O.; Loc, T. P., Further experiments on vortex formation around an oscillating and translating airfoil at large incidences, J. Fluid Mech., 225, 607-630 (1991)
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