×

Stabilization and shock-capturing parameters in SUPG formulation of compressible flows. (English) Zbl 1122.76061

Summary: The streamline-upwind/Petrov-Galerkin (SUPG) formulation is one of the most widely used stabilized methods in finite element computation of compressible flows. It includes a stabilization parameter that is known as \(\tau\). Typically the SUPG formulation is used in combination with a shock-capturing term that provides additional stability near the shock fronts. The definition of the shock-capturing term includes a shock-capturing parameter. In this paper, we describe, for the finite element formulation of compressible flows based on conservation variables, new ways for determining the \(\tau\) and the shock-capturing parameter. The new definitions for the shock-capturing parameter are much simpler than the ones based on the entropy variables, involve less operations in calculating the shock-capturing term, and yield better shock quality in test computations.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
76L05 Shock waves and blast waves in fluid mechanics
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Hughes, T.J.R.; Brooks, A.N., A multi-dimensional upwind scheme with no crosswind diffusion, (), 19-35 · Zbl 0423.76067
[2] Brooks, A.N.; Hughes, T.J.R., Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. methods appl. mech. engrg., 32, 199-259, (1982) · Zbl 0497.76041
[3] T.E. Tezduyar, T.J.R. Hughes, Development of time-accurate finite element techniques for first-order hyperbolic systems with particular emphasis on the compressible Euler equations, NASA Technical Report NASA-CR-204772, NASA, 1982, Available from: <http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19970023187_1997034954.pdf>. · Zbl 0535.76074
[4] T.E. Tezduyar, T.J.R. Hughes, Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations, in: Proceedings of AIAA 21st Aerospace Sciences Meeting, AIAA Paper 83-0125, Reno, Nevada, 1983.
[5] Hughes, T.J.R.; Tezduyar, T.E., Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations, Comput. methods appl. mech. engrg., 45, 217-284, (1984) · Zbl 0542.76093
[6] Tezduyar, T.E., Stabilized finite element formulations for incompressible flow computations, Adv. appl. mech., 28, 1-44, (1992) · Zbl 0747.76069
[7] Donea, J., A Taylor-Galerkin method for convective transport problems, Int. J. numer. methods engrg., 20, 101-120, (1984) · Zbl 0524.65071
[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] Le Beau, G.J.; Tezduyar, T.E., Finite element computation of compressible flows with the SUPG formulation, (), 21-27
[10] Tezduyar, T.E.; Park, Y.J., Discontinuity capturing finite element formulations for nonlinear convection-diffusion-reaction problems, Comput. methods appl. mech. engrg., 59, 307-325, (1986) · Zbl 0593.76096
[11] T.E. Tezduyar, Adaptive determination of the finite element stabilization parameters, in: Proceedings of the ECCOMAS Computational Fluid Dynamics Conference 2001 (CD-ROM), Swansea, Wales, United Kingdom, 2001.
[12] Tezduyar, T.E., Computation of moving boundaries and interfaces and stabilization parameters, Int. J. numer. methods fluids, 43, 555-575, (2003) · Zbl 1032.76605
[13] Tezduyar, T.; Sathe, S., Stabilization parameters in SUPG and PSPG formulations, J. computat. appl. mech., 4, 71-88, (2003) · Zbl 1026.76032
[14] Tezduyar, T.E., Finite element methods for fluid dynamics with moving boundaries and interfaces, (), (Chapter 17) · Zbl 0848.76036
[15] Tezduyar, T.E., Stabilized finite element methods for computation of flows with moving boundaries and interfaces, () · Zbl 0798.76037
[16] Tezduyar, T.E., Stabilized finite element methods for flows with moving boundaries and interfaces, HERMIS: int. J. comput. math. appl., 4, 63-88, (2003) · Zbl 1309.76135
[17] T.E. Tezduyar, Determination of the stabilization and shock-capturing parameters in SUPG formulation of compressible flows, in: Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004 (CD-ROM), Jyvaskyla, Finland, 2004.
[18] 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
[19] 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
[20] Tezduyar, T.E.; Osawa, Y., Finite element stabilization parameters computed from element matrices and vectors, Comput. methods appl. mech. engrg., 190, 411-430, (2000) · Zbl 0973.76057
[21] Aliabadi, S.K.; Tezduyar, T.E., Parallel fluid dynamics computations in aerospace applications, Int. J. numer. methods fluids, 21, 783-805, (1995) · Zbl 0862.76033
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.