Convergence of second-order schemes for isentropic gas dynamics

Chen, Gui Qiang; Liu, Jian-Guo

doi:10.1090/S0025-5718-1993-1185239-7

Convergence of second-order schemes for isentropic gas dynamics
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by Gui Qiang Chen and Jian-Guo Liu PDF

Math. Comp. 61 (1993), 607-627 Request permission

Abstract:

Convergence of a second-order shock-capturing scheme for the system of isentropic gas dynamics with ${L^\infty }$ initial data is established by analyzing the entropy dissipation measures. This scheme is modified from the classical MUSCL scheme to treat the vacuum problem in gas fluids and to capture local entropy near shock waves. Convergence of this scheme for the piston problem is also discussed.

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