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Massively parallel finite element computation of incompressible flows involving fluid-body interactions. (English) Zbl 0846.76048
We describe massively parallel finite element computations of unsteady incompressible flows involving fluid-body interactions. These computations are based on the deforming-spatial-domain/stabilized-space-time finite element formulation. Unsteady flows past a stationary NACA $$0012$$ airfoil are computed for Reynolds numbers $$1000$$, $$5000$$ and $$100 000$$. Significantly different flow patterns are observed for these three cases. The method is then applied to computation of the dynamics of an airfoil falling in a viscous fluid under the influence of gravity. All these computations were carried out on the Thinking Machines CM-200 and CM-5 supercomputers. The implicit equation systems arising from the finite element discretizations of these large-scale problems are solved iteratively by using the GMRES update technique with diagonal preconditioners.

##### MSC:
 76M10 Finite element methods applied to problems in fluid mechanics 76D05 Navier-Stokes equations for incompressible viscous fluids 65Y05 Parallel numerical computation
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##### References:
 [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 numerical 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] Mittal, S.; Tezduyar, T.E., A finite element study of incompressible flows past oscillating cylinders and aerofoils, Internat. J. numer. methods fluids, 15, 1073-1118, (1992) [4] Behr, M.; Johnson, A.; Kennedy, J.; Mittal, S.; Tezduyar, T.E., Computations of incompressible flows with implicit finite element implementations on the connection machine, University of minnesota supercomputer institute research report UMSI 92/102, (1992) · Zbl 0784.76046 [5] Hughes, T.J.R.; Franca, L.P., A new finite element formulation for computational fluid dynamics: VII. the Stokes problem with various well-posed boundary conditions: symmetric formulations that converge for all velocity/pressure spaces, Comput. methods appl. mech engrg., 65, 85-96, (1987) · Zbl 0635.76067 [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] Shakib, F., Finite element analysis of the compressible Euler and Navier-Stokes equations, () [8] Liou, J.; Tezduyar, Clustered element-by-element computations for fluid flow, (), 167-187 [9] 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 [10] Saad, Y.; Schultz, M.H., A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. sci. statist. comput., 7, 856-869, (1986) · Zbl 0599.65018 [11] Brooks, A.N.; Hughes, T.J.R., Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on incompressible Navier-Stokes equations, Comput. methods appl. mech. engrg., 32, 199-259, (1982) · Zbl 0497.76041 [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] Schlichting, H., Boundary layer theory, (1968), McGraw-Hill New York, translated by J. Kestin [14] Franca, L.P.; Frey, S.L.; Hughes, T.J.R., Stabilized finite element methods: I. application to the advective-diffusive model, Comput. methods appl. mech. engrg., 95, 253-276, (1992) · Zbl 0759.76040 [15] Franca, L.P.; Frey, S.L., Stabilized finite element methods: II. the incompressible Navier-Stokes equations, Comput. methods appl. mech. engrg., 99, 209-233, (1992) · Zbl 0765.76048 [16] Perkins, C.D.; Hage, R.E., Airplane performance stability and control, (1949), Wiley New York
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