Delta-shocks and vacuums in zero-pressure gas dynamics by the flux approximation
Delta-shocks and vacuums in zero-pressure gas dynamics by the flux approximation
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DOI：
10.1007/s11425-015-5034-0
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发表时间：
2014-08
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影响因子：
--
通讯作者：
Hanchun Yang;Jinjing Liu
中科院分区：
文献类型：
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作者：
Hanchun Yang;Jinjing Liu
本文首先通过用通量近似求解气体动力学中零压流的Riemann问题，构造了参数化的增量激波解和常密度解，然后证明了当通量扰动为零时，它们分别收敛到零压流的Delta激波解和真空态解。其次，我们用含压力的双参数通量近似求解等熵气体动力学欧拉方程的Riemann问题。此外，我们严格地证明了，当两参数通量摄动消失时，任何含有两个激波的Riemann解趋向于零压流的增量激波解；任何含有两个稀疏波的Riemann解趋向于零压流的双接触间断解，介于两者之间的非真空中间态趋于真空态。最后给出了三角波和真空态的形成过程的数值结果。
In this paper, firstly, by solving the Riemann problem of the zero-pressure flow in gas dynamics with a flux approximation, we construct parameterized delta-shock and constant density solutions, then we show that, as the flux perturbation vanishes, they converge to the delta-shock and vacuum state solutions of the zero-pressure flow, respectively. Secondly, we solve the Riemann problem of the Euler equations of isentropic gas dynamics with a double parameter flux approximation including pressure. Furthermore, we rigorously prove that, as the two-parameter flux perturbation vanishes, any Riemann solution containing two shock waves tends to a delta-shock solution to the zero-pressure flow; any Riemann solution containing two rarefaction waves tends to a two-contact-discontinuity solution to the zero-pressure flow and the nonvacuum intermediate state in between tends to a vacuum state. Finally, numerical results are given to present the formation processes of delta shock waves and vacuum states.