A unified finite element formulation for compressible and incompressible flows using augmented conservation variables

Computer Methods in Applied Mechanics and Engineering

Volumn 161, Issue 3-4, 1998, Pages 229-243

  Mittal, S ^a   Tezduyar, T ^b  

^a INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

^b University of Minnesota   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPRESSIBLE FLOW; CONVERGENCE OF NUMERICAL METHODS; EQUATIONS OF STATE OF LIQUIDS; FLUID MECHANICS; INCOMPRESSIBLE FLOW;

MACH NUMBER;

FINITE ELEMENT METHOD;

COMPRESSIBLE FLOW; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW;

COMPRESSIBLE FLOW; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW;

EID: 0032508401     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(97)00318-6     Document Type: Article

References (20)

1. [1] E. Turkel, Review of preconditioning methods for fluid dynamics, Technical Report 92-47, Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, September 1992.
2. [2] G. Hauke and T.J.R. Hughes, A unified approach to compressible and incompressible flows, Comput. Methods Appl. Mech. Engrg. 113 (1994) 389-395.
3. [3] G. Hauke, A unified approach to compressible and incompressible flows and a new entropy-consistent formulation of the K-epsilon model, Ph.D. Thesis, Department of Mechanical Engineering, Stanford University, 1995.
4. [4] J.M. Weiss and W.A. Smith, Preconditioning applied to variable and constant density flows, AIAA J. 33(11) (1995) 2050-2057.
5. [5] S.M.H. Karimian and G.E. Schneider, Pressure-based control-volume finite element method for flow at all speeds, AIAA J. 33(9) (1995) 1611-1618.
6. [6] T.E. Tezduyar and T.J.R. Hughes, Development of time-accurate finite element techniques for first-order hyperbolic systems with particular emphasis on the compressible Euler equations, Report prepared under NASA-Ames University Consortium Interchange, No. NCA2-OR745-104, 1982.
7. [7] T.E. Tezduyar and T.J.R. Hughes, Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations, in: Proc. AIAA 21st Aerospace Sciences Meeting, AIAA Paper 83-0125, Reno, Nevada, 1983.
8. [8] G.J. Le Beau, The finite element computation of compressible flows, Master's Thesis, Aerospace Engineering, University of Minnesota, 1990.
9. [9] G.J. Le Beau and T.E. Tezduyar, Finite element computation of compressible flows with the SUPG formulation, in: M.N. Dhaubhadel, M.S. Engelman and J.N. Reddy, eds., Advances in Finite Element Analysis in Fluid Dynamics, FED-Vol. 123 (ASME, New York, 1991) 21-27.
10. [10] G.J. Le Beau, S.E. Ray, S.K. Aliabadi and T.E. Tezduyar, SUPG finite element computation of compressible flows with the entropy and conservation variables formulations, Comput. Methods Appl. Mech. Engrg., 104 (1993) 27-42.
11. [11] S.K. Aliabadi and T.E. Tezduyar, Space-time finite element computation of compressible flows involving moving boundaries and interfaces, Comput. Methods Appl. Mech. Engrg. 107(1-2) (1993) 209-224.
12. [12] S.K. Aliabadi, S.E. Ray and T.E. Tezduyar, SUPG finite element computation of compressible flows with the entropy and conservation variables formulations, Comput. Mech. 11 (1993) 300-312.
13. [13] S. Mittal, Finite element computation of unsteady viscous compressible flows, Comput. Methods Appl. Mech. Engrg. (1997), to appear.
14. [14] R.L. Panton, Incompressible Flows (John Wiley and Sons, New York, 1984).
15. [15] T.J.R. Hughes and A.N. Brooks, A multi-dimensional upwind scheme with no crosswind diffusion, in: T.J.R. Hughes, ed., Finite Element Methods for Convection Dominated Flows, AMD-Vol. 34 (ASME, New York, 1979) 19-35.
16. [16] T.J.R. Hughes and T.E. Tezduyar, Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations, Comput. Methods Appl. Mech. Engrg. 45 (1984) 217-284.
17. [17] Y. Saad and M. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Scient. Statist. Comput. 7 (1986) 856-869.
18. [18] F. Shakib, Finite element analysis of the compressible Euler and Navier-Stokes equations, Ph.D. Thesis, Department of Mechanical Engineering, Stanford University, 1988.
19. [19] H.W. Liepmann and A. Roshko, Elements of Gas Dynamics (John Wiley and Sons, Inc., New York, 1957).
20. [20] M. Behr, D. Hastreiter, S. Mittal and T.E. Tezduyar, Incompressible flow past a circular cylinder: Dependence of the computed flow field on the location of the lateral boundaries, Comput. Methods Appl. Mech. Engrg. 123 (1995) 309-316.