Shock capturing approximations to the compressible Euler equations with geometric structure and related equations

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 49, Issue 3, 1998, Pages 341-362

  Chen, Gui Qiang ^a   Wang, Dehua ^b  

^a NORTHWESTERN UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Entropy solutions; Euler equations; Piston flow; Shock capturing method; Spherically symmetric flow; Transonic nozzle flow

Indexed keywords

EID: 0032369326     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000000050096     Document Type: Article

References (23)

1. J. M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rat. Mech. Anal. 63 (1977), 337-403.
2. G.-Q. Chen, Convergence of Lax-Friedrichs scheme for isentropic gas dynamics, III Acta Math. Sci. 8 (1988), 243-276 (in Chinese); 6 (1986), 75-120.
3. G.-Q. Chen, Convergence of Lax-Friedrichs scheme for isentropic gas dynamics, III Acta Math. Sci. 8 (1988), 243-276 (in Chinese); 6 (1986), 75-120.
4. G.-Q. Chen, Remarks on spherically symmetric solutions of the compressible Euler equations, Proc. Royal Soc. Edinburgh 127A (1997), 243-259.
5. G.-Q. Chen and J. Glimm, Global solutions to the compressible Euler equations with geometrical structure, Commun. Math. Phys. 180 (1996), 153-193.
6. G.-Q. Chen and J. Glimm, Global solutions to the cylindrically symmetric rotating motion of isentropic gases, Z. Angew. Math. Phys. 47 (1996), 353-372.
7. G.-Q. Chen and Ph. LeFloch, Isentropic Euler equations with general pressure law and related equations, Preprint, Northwestern University, 1997.
8. G.-Q. Chen and D. Wang , Convergence of shock capturing schemes for the compressible Euler-Poisson equations, Commun. Math. Phys. 179 (1996), 333-364.
9. C. Dafermos, Polygonal approximations of solutions of the initial-value problem for a conservation law, J. Math. Anal. Appl. 38 (1972), 33-41.
10. X. Ding, G.-Q. Chen and P. Luo, Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics (I)-(II), Acta Mathematica Scientia 7 (1987), 467-480; 8 (1988), 61-94 (in Chinese); 5 (1985), 415-432, 433-472.
11. X. Ding, G.-Q. Chen and P. Luo, Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics (I)-(II), Acta Mathematica Scientia 7 (1987), 467-480; 8 (1988), 61-94 (in Chinese); 5 (1985), 415-432, 433-472.
12. X. Ding, G.-Q. Chen and P. Luo, Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics (I)-(II), Acta Mathematica Scientia 7 (1987), 467-480; 8 (1988), 61-94 (in Chinese); 5 (1985), 415-432, 433-472.
13. X. Ding, G.-Q. Chen, and P. Luo, Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for the isentropic system of gas dynamics, Commun. Math. Phys. 121 (1989), 63-84.
14. R. DiPerna, Convergence of the viscosity method for isentropic gas dynamics, Commun. Math. Phys. 91 (1983), 1-30.
15. P. D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, CBMS. 11, SIAM, 1973.
16. P. L. Lions, B. Perthame, and E. Tadmor, Kinetic formulation of the isentropic gas dynamics and p-systems, Commun. Math. Phys. 163 (1994), 415-431.
17. P. L. Lions, B. Perthame, and E. Souganisdis, Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates, Comm. Pure Appl. Math. 49 (1996), 599-638.
18. T.-P. Liu, Nonlinear resonance for quasilinear hyperbolic equation, J. Math. Phys. 28 (1987), 243-260.
19. -1,q est compacte pour tout q < 2 J. Math. Pures Appl. 60 (1981), 309-322.
20. M. Slemrod, Resolution of the spherical piston problem for compressible isentropic gas dynamics via a self-similar viscous limit, Proc. Royal Soc. Edindurg 126A (1996), 1309-1340.
21. S. Takeno, Initial boundary value problem for isentropic gas dynamics, Proc. Roy. Soc. Edinburgh 120A (1992), 1-23.
22. L. Tartar, Compensated compactness and applications to partial differential equations, Research Notes in Mathematics, Nonlinear Analysis and Mechanics, ed. R.J. Knops, vol. 4, Pitman Press, New York 1979.
23. J.-H. Wang, X.-W. Li, and J.-Y. Huang, Lax-Friedrichs difference approximations to isentropic equations of gas dynamics, Systems Science and Mathematical Science 1 (1988), 109-118.