A Unified Coordinate System for Solving the Two-Dimensional Euler Equations

Journal of Computational Physics

Volumn 153, Issue 2, 1999, Pages 596-637

  Hui, W H ^a   Li, P Y ^a   Li, Z W ^a,b  

^a HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^b CHINA AERODYNAMICS RESEARCH AND DEVELOPMENT CENTER   (China)

Author keywords

Eulerian description; Hyperbolicity of euler equations; Inviscid compressible flow; Lagrangian description; Slip lines; Unified description

Indexed keywords

EULER EQUATIONS; LAGRANGE MULTIPLIERS;

CO-ORDINATE SYSTEM; EULER'S EQUATION; EULERIAN COORDINATE; EULERIAN DESCRIPTION; HYPERBOLICITY; HYPERBOLICITY OF EULER EQUATION; INVISCID COMPRESSIBLE FLOWS; LAGRANGIAN DESCRIPTION; SLIP LINES; UNIFIED DESCRIPTION;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 0001741885     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1999.6295     Document Type: Article

References (28)

1. D. H. Wagner, Equivalence of Euler and Lagrangian equations of gas dynamics for weak solutions, J. Differential Equations 68, 118 (1987).
2. A. Harten, The artificial compression method for computation of shocks and contact discontinuities: III. Self-adjusting hybrid schemes, Math. Comp. 32, 363 (1978).
3. A. Harten, ENO schemes with subcell resolution, J. Comput. Phys. 83, 148 (1989).
4. C. W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes II, J. Comput. Phys. 83, 32 (1989).
5. M. S. Liou, An extended Lagrangian method, J. Comput. Phys. 118, 294 (1995).
6. C. W. Hirt, A. A. Amsden, and J. L. Cook, An arbitrary Lagrangian-Eulerian computing method for all flow speeds, J. Comput. Phys. 14, 227 (1974).
7. W. Pracht, Calculating three-dimensional fluid flows at all speeds with an Eulerian-Lagrangian computing mesh, J. Comput. Phys. 17, 132 (1975).
8. L. G. Margolin, Introduction to "an arbitrary Lagrangian-Eulerian computing method for all flow speeds," J. Comput. Phys. 135, 198 (1997).
9. M. S. Hall, A comparison of first and second order rezoned and Lagrangian Godunov solutions, J. Comput. Phys. 90, 458 (1990).
10. C. Y. Loh and W. H. Hui, A new Lagrangian method for steady supersonic flow computation. Part I. Godunov scheme, J. Comput. Phys. 89, 207 (1990).
11. W. H. Hui and C. Y. Loh, A new Lagrangian method for steady supersonic flow computation. Part II. Slipline resolution, J. Comput. Phys. 103, 450 (1992).
12. W. H. Hui and C. Y. Loh, A new Lagrangian method for steady supersonic flow computation. Part III. Strong shocks, J. Comput. Phys. 103, 465 (1992).
13. W. H. Hui and Y. C. Zhao, A generalized Lagrangian method for solving the Euler equations, in Nonlinear Hyperbolic Problems: Theoretical, Applied and Computational Aspects, edited by A. Donato and F. Oliveri (Vieweg, Braunschwig, Germany, 1992), p. 336.
14. C. Y. Lepage and W. H. Hui, A shock-adaptive godunov scheme based on the generalized Lagrangian formulation, J. Comput. Phys. 122, 291 (1995).
15. W. H. Hui and D. L. Chu, Optimal grid for the steady Euler equations, Comput. Fluid Dyn. J. 4, 403 (1996).
16. C. Y. Loh and M. S. Liou, A new Lagrangian method for three-dimensional steady supersonic flows, J. Comput. Phys. 113, 224 (1994).
17. W. H. Hui and Y. He, Hyperbolicity and optimal coordinates for the three-dimensional supersonic Euler equations, SIAM J. Appl Math. 57, 893 (1997).
18. W. H. Hui, Generalized Lagrangian formulation of computational fluid dynamics in Computational Fluid Dynamics Review - 1995, edited by M. Hafez and K. Oshima (Wiley, New york, 1995), p. 382.
19. E. Godlewski and P.-A. Raviart, Numerical Approximation of Hyperbolic System of Conservation Laws (Springer, New York, 1996).
20. H. O. Kreiss and J. Lorenz, Initial-Boundary Value Problems and the Navier-Stokes Equations (Academic Press, San Diego, 1989).
21. W. H. Hui and S. Koudriakov, The role of coordinates in the computation of discontinuities in one-dimensional Flow, submitted for publication.
22. R. P. Fedkiew, B. Merriman, and S. Osher, Efficient characteristic projection upwind difference schemes for hyperbolic systems, J. Comput. Phys. 141, 22 (1998).
23. S. K. Godunov, Difference method of nuemrical computations of discontinuous solutions in hydrodynamic equations, Math. Sbornik 47, 271 (1959).
24. B. Van Leer, Towards the ultimate conservative difference scheme, V. A second order sequel to Godunov's method, J. Comput. Phys. 32, 234 (1979).
25. M. G. Crandall and A. Majda, Monotone difference approximations for scalar conservation laws, Math. Comp. 34, 1 (1980).
26. G. Strang, On the construction and comparison of difference schemes, SIAM J. Numer. Anal. 5, 506 (1968).
27. M. Van Dyke, An Album of Fluid Motion (The Parabolic Press, Stanford, CA, 1982), p. 143.
28. C. Y. Loh and W. H. Hui, A new Lagrangian method for time-dependent inviscid flow computation, SIAM J. Sci. Comput., in press (1999).