Automatic directional refinement in adaptive analysis of compressible flows. (English) Zbl 0810.76045

In such local phenomena as shocks and boundary layers, etc., the discretization errors are directional and the use of elongated elements is obvious if economy is to be achieved. We present a procedure which achieves the combination of such locally structured meshes with a general unstructured mesh generator in an automatic and fully adaptive manner. The procedure is illustrated in the context of compressible, viscous and inviscid, flows but has obvious applications in other (solid mechanics) problems involving localization.


76M10 Finite element methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
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[1] Peraire, J. Comput. Phys. 72 (1987)
[2] Peraire, Int. j. numer. methods eng. 25 pp 23– (1988)
[3] Hassan, Comput. Methods Appl. Mech. Eng. 76 pp 245– (1989)
[4] ’Finite element computations of high speed viscous compressible flows’, Ph. D. thesis, University College of Swansea, 1990.
[5] Zienkiewicz, Int. j. numer. methods eng. 24 pp 337– (1987)
[6] Zienkiewicz, Int. j. numer. methods eng. 26 pp 2135– (1988)
[7] Löhner, Comput. Methods Appl. Mech. Eng. 75 pp 195– (1989)
[8] Wu, Comput. Mech. 6 pp 259– (1990)
[9] Probert, Int. j. numer. methods eng. 32 pp 1145– (1991)
[10] Donea, Int. j. numer. methods eng. 20 pp 101– (1984)
[11] Zienkiewicz, Int. j. numer. methods eng. 35 pp 457– (1992)
[12] Löhner, Comput. Methods Appl. Mech. Eng. 51 pp 441– (1985)
[13] and , Finite Element Method, 4 edn., Vol II, McGraw-Hill, 1991.
[14] Johnson, Comput. Methods Appl. Mech. Eng. 101 pp 143– (1992)
[15] and , ’Adaptive finite element methods for conservation laws based on a posteriori error estimates’, Report no. 1992-31/ISSN 0347-2809, Department of Mathematics, Chalmers University of Technology and the University of Goteborg, 1992.
[16] and , ’A 3D finite element multigrid solver for the Euler equations’, AIAA paper 92-0449, 1992.
[17] Peraire, Rev. Int. Methods Numer. Calc. Diseno Ing. 8 pp 215– (1992)
[18] ’A generalized compressible flow system for 2-dimensional geometries’, Report, Computational Dynamics Research, 1992.
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