On the 2-D Riemann Problem for the Compressible Euler Equations II. Interaction of Contact Discontinuities

Discrete and Continuous Dynamical Systems

Volumn 6, Issue 2, 2000, Pages 419-430

  Chang, Tung ^a   Chen, Gui Qiang ^b   Yang, Shuli ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^b NORTHWESTERN UNIVERSITY   (United States)

Author keywords

2 D Riemann problem; Contact discontinuities; Euler equations; Interaction of waves; Rarefaction waves; Shock waves; Transonic flow; Upwind averaging schemes; Vortices

Indexed keywords

EID: 0034405332     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2000.6.419     Document Type: Article

References (16)

1. [CY1] T. Chang, G.-Q. Chen, and S. Yang, On the 2-D Riemann problem for the compressible Euler equations I. Interaction of shocks and rarefaction waves, Discrete and Continuous Dynamical Systems, 1 (1995), 555-584.
2. [CY2] T. Chang, G.-Q. Chen, and S. Yang, 2-D Riemann problem in gas dynamics and formation of spiral, In: Nonlinear Problems in Engineering and Science - Numerical and Analytical Approach (Beijing, 1991), 167-179 (1992), Science Press: Beijing.
3. [CH] T. Chang and L. Hsiao, The Riemann Problem and Interaction of Waves in Gas Dynamics, Longman Scientific and Technical (Pitman Monographs No. 41), Essex, 1989.
4. [CF] R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, Springer-Verlag: New York, 1948.
5. [GM] J. Glimm and A. Majda, Multidimensional Hyperbolic Problems and Computations, IMA Volume 29, Springer-Verlag: New York, 1991.
6. [K] D. J. Korchinski, Solution of a Riemann problem for a 2 × 2 system of conservation laws possessing no classical weak solutions, Thesis, Adelphi University, 1977.
7. [GK] J. Glimm, C. Klingenberg, O. McBryan, B. Plohr, D. Sharp, and S. Yaniv, Front tracking and two-dimensional Riemann problems, Adv. Appl. Math. 6 (1985), 259-290.
8. [La] P. D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, SIAM, Philadelphia, 1973.
9. [LL] P. D. Lax and X.-D. Liu, Solutions of two dimensional Riemann problem of gas dynamics by positive schemes, SIAM Sci. Comput. 19 (1998), 319-340.
10. [LZY] J. Li, T. Zhang, and S. Yang, The Two-Dimensional Riemann Problem in Gas Dynamics, Longman (Pitman Monographs 98): Essex, 1998.
11. [SC] C. W. Schulz-Rinne, J. P. Collins, and H. M. Glaz, Numerical solution of the Riemann problem for two-dimensional gas dynamics, SIAM J. Sci. Comput. 14 (1993), 1394-1414.
12. [SZ] W. Sheng and T. Zhang, The Riemann problem for the transportation equations in gas dynamics, Mem. Amer. Math. Soc. 654, 1999.
13. [TZ] D. C. Tan and T. Zhang, Two-dimensional Riemann problem for a hyperbolic system of non-linear conservation laws (I)-(II), J. Diff. Eqs. 111 (1994), 203-282.
14. [TZZ] D. C. Tan, T. Zhang, and Y.-X. Zheng, Delta-shock waves as limits of vanishing viscosity for hyperbolic systems of conservation laws, J. Diff. Egs. 112 (1994), 1-32.
15. [YZ] S.-L. Yang and T. Zhang, The MMB difference solutions of 2-D Riemann problems for a 2 × 2 hyperbolic system of conservation laws, Impact Comput. Sci. Eng. 3 (1991), 146-180.
16. [ZZ] T. Zhang and Y.-X. Zheng, Conjecture on the structure of solutions of the Riemann problem for two-dimensional gas dynamics systems, SIAM J. Math. Anal. 21 (1990), 593-630.