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Shock capturing approximations to the compressible Euler equations with geometric structure and related equations (1998)

Chen, G.-Q. ; Wang, D.

Springer

Zeitschrift für angewandte Mathematik und Physik 49 (1998), S. 341-362

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ISSN: 0044-2275

Keywords: Key words. Entropy solutions, shock capturing method, transonic nozzle flow, spherically symmetric flow, piston flow, Euler equations.

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract. In this paper we analyze a shock capturing method, developed by Chen-Glimm [4], to construct approximate solutions of the transonic nozzle flow and the spherically symmetric flow for the compressible Euler equations and related equations. The $L^\infty$ -stability, $H^{-1}$ -compactness, and convergence of the approximate solutions are proved for any adiabatic exponent $\gamma〉1$ for the isentropic Euler equations. The corresponding global solutions are obtained for arbitrarily large $L^\infty$ initial data.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s000000050096

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