Delta-shocks and vacuum states in the vanishing pressure limit of solutions to the isentropic Euler equations for modified Chaplygin gas ☆
Delta-shocks and vacuum states in the vanishing pressure limit of solutions to the isentropic Euler equations for modified Chaplygin gas ☆
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DOI：
10.1016/j.jmaa.2013.12.025
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发表时间：
2014-05
影响因子：
1.3
通讯作者：
Hanchun Yang;Jinhuan Wang
中科院分区：
文献类型：
--
作者：
Hanchun Yang;Jinhuan Wang
分析了当双参数压力消失时，修正 Chaplygin 气体的等熵欧拉方程解中的浓集和空化现象以及 δ 激波和真空态的形成。首先，解析求解修正 Chaplygin 气体的等熵欧拉方程的黎曼问题。其次，严格证明，当压力消失时，修正 Chaplygin 气体的等熵欧拉方程的任何双激波黎曼解都趋向于输运方程的 δ 激波解，并且两个激波之间的中间密度趋向于形成 δ 激波的加权 δ 测度；修正 Chaplygin 气体的等熵欧拉方程的任何二稀疏波黎曼解都趋向于输运方程的二接触不连续解，两个稀疏波之间的非真空中间态趋向于真空态。最后，一些数值结果显示了随着压力降低，δ-激波和真空状态的形成。
The phenomena of concentration and cavitation and the formation ofδ-shocks and vacuum states in solutions to the isentropic Euler equations for a modified Chaplygin gas are analyzed as the double parameter pressure vanishes. Firstly, the Riemann problem of the isentropic Euler equations for a modified Chaplygin gas is solved analytically. Secondly, it is rigorously shown that, as the pressure vanishes, any two-shock Riemann solution to the isentropic Euler equations for a modified Chaplygin gas tends to aδ-shock solution to the transport equations, and the intermediate density between the two shocks tends to a weightedδ-measure that forms theδ-shock; any two-rarefaction-wave Riemann solution to the isentropic Euler equations for a modified Chaplygin gas tends to a two-contact-discontinuity solution to the transport equations, the nonvacuum intermediate state between the two rarefaction waves tends to a vacuum state. Finally, some numerical results exhibiting the formation ofδ-shocks and vacuum states are presented as the pressure decreases.