Shock capturing and global solutions to the compressible Euler equations with geometrical structure. (English) Zbl 0964.35517
Glimm, J. (ed.) et al., Proceedings of the 5th international conference on hyperbolic problems: theory, numerics, applications, New York, NY, USA, June 13-17, 1994. Singapore: World Scientific. 101-109 (1996).
Summary: We are concerned with global solutions and corresponding shock capturing approximations to the Euler equations of compressible gas dynamics with geometrical structure. Recent developments in this direction are reviewed and the role of the shock capturing approach in solving the Euler equations is discussed. Some efficient shock capturing methods as well as their convergence and consistency are analyzed to compute the corresponding compressible flows and to construct correct approximate solutions. For the entire collection see [Zbl 0903.00041
|35Q35||PDEs in connection with fluid mechanics|
|76L05||Shock waves; blast waves (fluid mechanics)|
|76N15||Gas dynamics, general|