A unified approach for inviscid compressible and nearly incompressible flow by least-squares finite element method

Applied Numerical Mathematics

Volumn 44, Issue 1-2, 2003, Pages 183-199

  Moussaoui, Farid ^a  

^a EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

ENTHALPY; FINITE ELEMENT METHOD; INCOMPRESSIBLE FLOW; INTERPOLATION; LEAST SQUARES APPROXIMATIONS; TEMPERATURE;

INVISCID COMPRESSIBLE FLOWS;

COMPRESSIBLE FLOW;

EID: 0037214097     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(02)00148-4     Document Type: Article

References (48)

1. Baruzzi G., Habashi W.G., Guèvremont W.G., Hafez M.M. A second order finite element method for the solution of the transonic Euler and and Navier-Stokes equations. Internat. J. Numer. Methods Fluids. 20:1995;671-693.
2. Le Beau G.J., Ray S.E., Aliabadi S.K., Tezduyar T.E. SUPG finite element computation of compressible flows with the entropy and conservation variables formulations. Comput. Methods Appl. Mech. Engrg. 104:1993;397-422.
3. M. Bernadou, et al., Modulef: Une bibliothèque modulaire d'éléments finis, Technical Report, INRIA, 1988.
4. Bochev P.B., Gunzburger M.D. Analysis of least-sqaures finite element methods for the Stokes equations. Math. Comp. 63:1994;479-506.
5. Briley W.R., McDonald H., Shamroth S.J. A low Mach number Euler formulation and application to time iterative LBI schemes. AIAA J. 21:1983;1467-1469.
6. Bruneau C.H., Chattot J.J., Laminie J. Computation of 3D vortex flows past a flat plate at incidence through a variational approach of the full steady Euler equations. Internat. J. Numer. Methods Fluids. 9:1989;305-323.
7. Bruneau C.H., Chattot J.J., Laminie J., Guiu-Roux J. Finite element least square method for solving full steady euler equations in a plane nozzle. Krause E. 8th International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Phys. 170:1983;161-166 Springer-Verlag, Berlin.
8. Bruneau C.H., Laminie J. A method to compute 3D hypersonic flows with Euler model. Comput. Fluid Dyn. J. 1:(4):1993;347-360.
9. Chattot J.J., Guiu-Roux J., Laminie J. Finite element calculation of steady transonic flow in nozzles using primary variables. Proceedings Seventh International Conference on Numerical Methods in Fluid Dynamics, Stanford, CA. Lecture Notes in Phys. 141:1980;Springer-Verlag, Berlin.
10. Chattot J.J., Guiu-Roux J., Laminie J. Numerical solution of a first-order conservation equation by a least square method. Internat. J. Numer. Methods Fluids. 2:1982;209-219.
11. Chattot J.J., Guiu-Roux J., Laminie J. Numerical solution of a first-order conservation equation by a least square method. Internat. J. Numer. Methods Fluids. 2:1982;209-219.
12. Choi Y.H., Merkle C.L. The application of precontioning in viscous flows. J. Comput. Phys. 105:1988;293-311.
13. Chorin A.J. A numerical method for solving incompressible viscous flow problems. J. Comput. Phys. 2:1967.
14. Fletcher C.A.J. A primitive variable finite element formulation for inviscid compressible flow. J. Comput. Phys. 33:1979.
15. M.M. Hafez, Variational approaches to CFD: Applications to potential, Euler and Navier-Stokes equations, in: 24th Computational Fluid Dynamics, VKI Lecture Series on Computational Fluid Dynamics. VKI LS 1993-04, VKI, Rhode-Saint-Genèse, March 1993.
16. Harlow F.H., Amsden A.A. A numerical fluid dynamics calculation method for all speeds. J. Comput. Phys. 8:1971;197-213.
17. Hauke G., Hughes T.J.R. A comparative study of different sets of variables for solving compressible and incompressible flows. Comput. Methods Appl. Mech. Engrg. 153:1998;1-44.
18. Huang Y., Lerat A. Second-order upwinding through a characteristic time-step matrix for compressible flow calculations. J. Comput. Phys. 142:(2):1998;445-472.
19. Hughes T.J.R., Franca L.P., Mallet M. A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics. Comput. Methods Appl. Mech. Engrg. 54:1986;223-234.
20. Issa R.I. Solution of the implicitly discetized fluid flow equations by operator-splitting. J. Comput. Phys. 62:1986;40-65.
21. Jiang B.N. A stable least-squares finite element method for nonlinear hyperbolic equations. Internat. J. Numer. Methods Fluids. 8:1988;933-942.
22. Jiang B.N. A least-squares finite element method for incompressible Navier-Stokes problems. Internat. J. Numer. Methods Fluids. 14:1992;843-859.
23. Jiang B.N. The Least-Squares Finite Element Method. Theory and Applications in CFD and Electromagnetics. 1998;Springer-Verlag, Berlin.
24. Jiang B.N., Povinelli L.A. Large scale compuation of incompressible viscous flow by least-squares finite element method. Comput. Methods Appl. Mech. Engrg. 114:1990;213-231.
25. Jiang B.N., Povinelli L.A. Least-squares finite element method for fluid dynamics. Comput. Methods Appl. Mech. Engrg. 81:1990;13-37.
26. Kariman S.M.H., Shneider G.E. A pressure-based control volume finite element method for flow at all speeds. AIAA J. 33:1995;1611-1618.
27. Klainerman, Majda. Compressible and incompressible fluids. Commun. Pure Appl. Math. 25:1982;629-651.
28. Kreiss H.O., Lorenz J., Naughton M.J. Convergence of the solutions of the compressible to the solutions of the incompressible Navier-Stokes equations. Adv. Appl. Math. 12:1991;187-214.
29. Lefebvre D., Peraire J., Morgan K. Finite element least-squares solution of the Euler equations using linear and quadratic approximations. Internat. J. Comput. Fluid Dynam. 2:1992;209-219.
30. Majda A. Compressible Fluid Flow and Systems of Conservation Laws in Several Spaces Variables. 1984;Springer-Verlag, Berlin.
31. Merkle C.L., Choi Y.H. Computation of low speed flow with heat addition. AIAA J. 25:1987;831-838.
32. Merkle C.L., Choi Y.H. Computation of low speed flow with heat addition. Internat. J. Numer. Methods Engrg. 25:1988;293-311.
33. Mittal S., Tezduyar T. A unified finite element formulation for compressible and incompressible flows using augmented conservation variables. Comput. Methods Appl. Mech. Engrg. 161:1998;229-243.
34. Morgan K., Löhner R., Zienkiewicz O.C. An adaptive finite element procedure for compressible high speed flows. Comput. Methods Appl. Mech. Engrg. 51:1985;441-465.
35. Nigro N., Storti M., Idelsohn S. GMRES physics-based preconditioner for all Reynolds and Mach numbers: Numerical examples. Internat. J. Numer. Methods Fluids. 25:1997;1347-1371.
36. Nigro N., Storti M., Idelsohn S., Tezduyar T. Physics based GMRES preconditioner for compressible and incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 154:1998;203-228.
37. Reddy J.N. An Introduction to the Finite Element Method. 2nd Edition:1993;McGraw-Hill, New York.
38. F. Shakib, Finite element analysis of the compressible Euler and Navier-Stokes equations, Ph.D. Thesis, Department of Mechanical Engineering, Stanford University, Stanford, CA, 1988.
39. D. Sidilkover, T.W. Roberts, R.C. Swanson, Textbook multigrid efficiency for the steady euler equations, Technical Report AIAA 97-1949, AIAA Paper, 1997.
40. Turkel E. Preconditioning methods for solving the incompressible and low speed compressible equations. J. Comput. Phys. 72:1987;277-298.
41. Turkel E. Review of preconditioning method for fluid dynamics. Appl. Numer. Math. 12:1993;257-284.
42. E. Turkel, Review of preconditioning techniqes for fluid dynamics, Technical Report 93-42, ICASE, 1993.
43. Turkel E., Fiterman A., van Leer B. Preconditioning and the limit to the incompressible flow equations. Hafez M., Caughey D. Computing for the Future: Advances and Prospects for Computational Aerodynamics. 1994;215-234 Wiley, New York. (see also ICASE Report 93-42).
44. B. van Leer, W.T. Lee, P.L. Roe, Characteristic time-stepping or local preconditioning of the Euler equations, Technical Report 91-1552-CP, AIAA Paper, June 1991.
45. C. Viozat, Implicit upwind schemes for low Mach number compressible flow, Technical Report RR-2084, INRIA, 1997.
46. Volpe G. Performance of compressible codes at low Mach number. AIAA J. 31:(1):1993;49-56.
47. Yu S.T., Jiang B.N., Wu J. A div-curl-grad formulation for three-dimensional low-Mach flows solved by the least-squares finite element method. Comput. Methods Appl. Mechanics Engrg. 1997.
48. Yu S.T., Jiang B.N., Wu J., Liu N.S. The least-squares finite element method for low Mach number compressible viscous flows. Internat. J. Numer. Methods Engrg. 38:1995;3591-3610.