An adaptive least-squares method for the compressible Euler equations

International Journal for Numerical Methods in Fluids

Volumn 31, Issue 7, 1999, Pages 1121-1139

  Taghaddosi, F ^a   Habashi, W G ^a   Guevremont G ^a   Ait Ali Yahia, D ^a  

^a Dept of Electrical and Computer Engineering   (Canada)

Author keywords

Artificial viscosity; Euler equations; Grid adaption; Least squares method

Indexed keywords

COMPRESSIBLE FLOW; EULER FLOW; MATHEMATICAL METHOD; VISCOSITY;

FINITE ELEMENT METHOD; LEAST SQUARES APPROXIMATIONS; VISCOSITY;

EULER EQUATIONS;

COMPUTATIONAL FLUID DYNAMICS;

EID: 0033571991     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0363(19991215)31:7<1121::AID-FLD913>3.0.CO;2-R     Document Type: Article

References (29)

1. D. Ait-Ali-Yahia, W.G. Habashi, A. Tam, M.-G. Vallet and M. Fortin, 'A directionally-adaptive methodology using an edge-based error estimate on quadrilateral grids', Int J. Numer. Methods Fluids, 23, 673-690 (1996).
2. O. Axelsson, Iterative Solution Methods, Cambridge University Press, Cambridge, 1994.
3. G.S. Baruzzi, W.G. Habashi and M.M. Hafez, 'Finite element solutions of the Euler equations for transonic external flows', AIAA J., 29, 1886-1893 (1991).
4. G.S. Baruzzi, W.G. Habashi and M.M. Hafez, 'A second-order finite element method for the solution of the transonic Euler and Navier-Stokes equations', Int. J. Numer. Methods Fluids, 20, 671-693 (1995).
5. 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. Eng., 104, 397-422 (1993).
6. A.L. Brooks and T.J.R. Hughes, 'Streamline upwind Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations', Comput. Methods Appl. Mech. Eng., 32, 199-259 (1982).
7. Ch.H. Bruneau, J. Laminie and J.J. Chattot, 'Computation of 3D vortex flows past a flat plate at incidence through a variational approach of the full steady Euler equations', Int. J. Numer. Methods Fluids, 9, 305-323 (1989).
8. G.F. Carey and B.-N. Jiang, 'Least-squares finite element method and preconditioned conjugate gradient solution', Int. J. Numer. Methods Eng., 24, 1283-1296 (1987).
9. G.F. Carey and B.-N. Jiang, 'Least-squares finite elements for first-order hyperbolic systems', Int. J. Numer. Methods Eng., 26, 81-93 (1988).
10. S. Eidelman, P. Colella and R.P. Shreeve, 'Application of the Godunov method and its second-order extension to cascade flow modeling', AIAA J., 22, 1609-1615 (1984).
11. C.A.J. Fletcher, 'A primitive variable finite element formulation for inviscid compressible flow', J. Comput. Phys., 33, 301-312 (1979).
12. P.A. Gnoffo, 'A finite-volume, adaptive grid algorithm applied to planetary entry flowfields', AIAA J., 21, 1249-1254 (1983).
13. 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. Eng., 45, 217-284 (1984).
14. T.J.R. Hughes, M. Mallet and A. Mizukami, 'A new finite element formulation for computational fluid dynamics: II. Beyond SUPG', Comput. Methods Appl. Mech. Eng., 54, 341-355 (1986).
15. B.-N. Jiang and G.F. Carey, 'Adaptive refinement for least-squares finite elements with element-by-element conjugate gradient solution', Int. J. Numer. Methods Eng., 24, 569-580 (1987).
16. B.-N. Jiang and G.F. Carey, 'Least-squares finite element methods for compressible Euler equations', Int. J. Numer. Methods Fluids, 10, 557-568 (1990).
17. B.-N. Jiang and L.A. Povinelli, 'Least-squares finite element method for fluid dynamics', Comput. Methods Appl. Mech. Eng., 81, 13-37 (1990).
18. Y. Jiang, C.P. Chen and H.M. Shang, 'A new pressure-velocity coupling procedure for inviscid and viscous flows at all speeds', Proceedings of the Fourth Int. Sym. on Computational Fluid Dynamics, Vol. 1, University of California, Davis, September 9-12, 1991, pp. 545-550.
19. D. Lefebvre and J. Peraire, 'Finite element least squares solution of the Euler equations using linear and quadratic approximations', Int. J. Comp. Fluid Dyn., 1, 1-23 (1993).
20. R. Löhner, K. Morgan and O.C. Zienkiewicz, 'The solution of non-linear hyperbolic equation systems by the finite element method', Int. J. Num. Meth. Fluids, 4, 1043-1063 (1984).
21. P.P. Lynn and S.K. Arya, 'Use of the least squares criterion in the finite element formulation', Int. J. Num. Meth. Eng., 6, 75-88 (1973).
22. K. Nakahashi and G.S. Diewert, 'Self-adaptive-grid method with application to airfoil flow', AIAA J., 25, 513-520 (1987).
23. H. Nguyen and J. Reynen, 'A space-time least-square finite element scheme for advection-diffusion equations', Comp. Meth. Appl. Mech. Eng., 42, 331-342 (1984).
24. R.-H. Ni, 'A multiple grid scheme for solving the Euler equations', AIAA J., 20, 1565-1571 (1982).
25. J.T. Oden, T. Strouboulis and Ph. Devloo, 'Adaptive finite element methods for high-speed compressible flows', Int. J. Num. Meth. Fluids, 7, 1211-1228 (1987).
26. J. Peraire, M. Vahdati, K. Morgan and O.C. Zienkiewicz, 'Adaptive remeshing for compressible flow computations', J. Comp. Phys., 72, 449-466 (1987).
27. J.F. Polk and P.P. Lynn, 'A least squares finite element approach to unsteady gas dynamics', Int. J. Num. Meth. Eng., 12, 3-10 (1978).
28. J.N. Reddy, An Introduction to the Finite Element Method, McGraw-Hill, New York, 1993.
29. L.Q. Tang and T.T.H. Tsang, 'An efficient least-squares finite element method for incompressible flows and transport processes', Int. J. Comp. Fluid Dyn., 4, 21-39 (1995).