Delta Shock Waves as Flux-Approximation Limit of Solutions to the Modified Chaplygin Gas Equations
Delta Shock Waves as Flux-Approximation Limit of Solutions to the Modified Chaplygin Gas Equations
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DOI：
10.1007/s10440-019-00280-2
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发表时间：
2019-07
影响因子：
1.6
通讯作者：
Jinjing Liu;Jie Liang;Hanchun Yang
中科院分区：
文献类型：
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作者：
Jinjing Liu;Jie Liang;Hanchun Yang
通过在修正的Chaubergin气体方程中引入包含压力的三参数通量摄动，证明了当三参数通量摄动为零时，扰动修正的Chaubergin气体方程的任意两激波Riemann解和任意两稀疏波Riemann解分别趋向于输运方程的δ激波解和真空解.证明了当双参数通量扰动为零时，扰动修正的Chaubergin气体方程的任意两激波Riemann解在一定条件下都趋于广义Chaubergin气体方程的δ激波解.此外，我们还证明了，当单参数通量扰动消失时，满足一定初值的任意双激波解和扰动后的任意参数化Delta激波解都趋向于Delta激波解.最后，我们展示了一些有代表性的数值模拟，以证实理论分析。
By introducing a triple parameter flux perturbation including pressure in the modified Chaplygin gas equations, we prove that, as the triple parameter flux perturbation vanishes, any two-shock Riemann solution and any two-rarefaction-wave Riemann solution to the perturbed modified Chaplygin gas equations tend to a delta-shock and a vacuum solution to the transport equations, respectively. Then we show that, as a double parameter flux perturbation vanishes, any two-shock Riemann solution under a certain condition to the perturbed modified Chaplygin gas equations tends to a delta shock wave solution to the generalized Chaplygin gas equations. In addition, we also show that, as a single parameter flux perturbation vanishes, any two-shock solution satisfying certain initial data and any parameterized delta shock wave solution to the perturbed generalized Chaplygin gas equations tend to a delta shock wave solution to the generalized Chaplygin gas equations. Finally, we exhibit some representative numerical simulations to confirm the theoretical analysis.