The Riemann problem for one dimensional generalized Chaplygin gas dynamics

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:403

Article

Wang, Guodong

关键词: Generalized Chaplygin gas;    Riemann problem;    Delta-shock wave;    Generalized Rankine-Hugoniot conditions;    Numerical simulations;   

DOI  :  10.1016/j.jmaa.2013.02.026

来源: Elsevier

【 摘 要 】

The Riemann problem for one dimensional generalized Chaplygin gas dynamics is considered. Its two characteristic fields are genuinely nonlinear, but the nonclassical solutions appear. The formation of mechanism for delta-shock is analyzed, that is the one-shock curve and the two-shock curve do not intersect each other in the phase plane. The Riemann solutions are constructed, and the generalized Rankine-Hugoniot conditions and the delta-entropy condition are clarified. By the interaction of the delta-shock wave with the elementary waves, the generalized Riemann problem for this system is presented. Furthermore, by studying the limits of the solutions as perturbed parameter epsilon approaches zero, one can observe that the Riemann solutions are stable for such perturbations of the initial data. Some numerical simulations are given to illustrate our analysis. Crown Copyright (C) 2013 Published by Elsevier Inc. All rights reserved.

【 授权许可】

Free