## Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces.(English)Zbl 0848.76036

Summary: We present strategies to update the mesh as the spatial domain changes its shape in computations of flow problems with moving boundaries and interfaces. These strategies are used in conjunction with the stabilized space-time finite element formulations introduced earlier for computation of flow problems with free surfaces, two-liquid interfaces, moving mechanical components, and fluid-structure and fluid-particle interactions. In these mesh update strategies, based on the special and automatic mesh moving schemes, the frequency of remeshing is minimized to reduce the projection errors and to minimize the cost associated with mesh generation and parallelization set-up. These costs could otherwise become overwhelming in three-dimensional problems. We present several examples of these mesh update strategies being used in massively parallel computation of incompressible flow problems.

### MSC:

 76M10 Finite element methods applied to problems in fluid mechanics 65Y05 Parallel numerical computation
Full Text:

### References:

 [1] Tezduyar, T. E.; Behr, M.; Liou, J., A new strategy for finite element computations involving moving boundaries and interfaces — the deformable-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 boundaries and interfaces — the deformable-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] Aliabadi, S. K.; Ray, S. E.; Tezduyar, T. E., SUPG finite element computation of viscous compressible flows based on the conservation and entropy variables formulations, Comput. Mech., 11, 300-312 (1993) · Zbl 0772.76032 [5] 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., 75, 173-189 (1989) · Zbl 0697.76100 [6] Tezduyar, T. E.; Behr, M.; Mittal, S.; Johnson, A. A., Computation of unsteady incompressible flows with the stabilize finite element methods: space-time formulations, iterative strategies and massively parallel implementations, (New Methods in Transient Analysis, AMD, Vol. 143 (1992), ASME) [7] Johan, Z., Data parallel finite element techniques for large-scale computational fluid dynamics, (Ph.D. Thesis (1992), Department of Mechanical Engineering, Stanford University) [8] Tezduyar, T. E.; Aliabadi, S. K.; Behr, M.; Johnson, A. 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)) · Zbl 0848.76040 [9] Aliabadi, S. K.; Tezduyar, T. E., Space-time finite element computation of compressible flows involving moving boundaries and interfaces, Comput. Methods Appl. Mech. Engrg., 107, 209-223 (1993) · Zbl 0798.76037 [10] Behr, M.; Johnson, A. 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 [11] Tezduyar, T. E.; Aliabadi, S. K.; Behr, M.; Johnson, A. A.; Mittal, S., Parallel finite element computation of 3D flows, IEEE Computer, 27-36 (October 1993) [12] 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 [13] Behr, M.; Tezduyar, T. E., Finite element solution strategies for large-scale flow simulations, Comput. Methods Appl. Mech. Engrg., 112, 3-24 (1994) · Zbl 0846.76041 [14] Aliabadi, S. K.; 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 [15] Lynch, D. R., Unified approach to simulation on deforming elements with application to phase change problems, J. Comput. Phys., 47, 187-411 (1982) · Zbl 0486.65063 [16] Reu, T.; Ying, S. X., Hybrid grid approach to study dynamic stall, AIAA J., 30, 2670-2676 (1992) [17] Leal, L. G., Computational studies of drop and bubble dynamics in a viscous fluid, (AIP Conf. Proc. 197: Drops and Bubbles (3rd Internat. Colloquium). AIP Conf. Proc. 197: Drops and Bubbles (3rd Internat. Colloquium), Monterey, CA (1988)) · Zbl 1186.76314 [18] Clift, R.; Grace, J.; Weber, M., Bubbles, Drops, and Particles (1978), Academic Press [19] Hecht, F.; Salel, E., $$Emc^2$$ un logiciel d’édition de maillages et de contours bidimensionnels, RT n° 118, INRIA (April, 1990) [20] Videv, T.; Doi, Y., Numerical study of flow and thrust produced by a pitching 2D hydrofoil, J. Soc. Naval Archives of Japan, 172 (1992) [21] Videv, T.; Doi, Y.; Mori, K., Numerical investigation of flow and thrust of an oscillating 2D hydrofoil, (6th Internat. Conf. on Numerical Ship Hydrodynamics. 6th Internat. Conf. on Numerical Ship Hydrodynamics, Iowa (1993)) [22] Harlow, F. H.; Welch, J. E.; Shannon, J. P.; Daly, B. J., The MAC Method, Los Alamos Scientific Laboratory Report LA-3425 (1965)
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.