Delta-shocks and vacuums in zero-pressure gas dynamics by the flux approximation  

作　　者：YANG HanChun LIU JinJing 

机构地区：[1]Department of Mathematics,Yunnan University

出　　处：《Science China Mathematics》2015年第11期2329-2346,共18页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11361073)

摘　　要：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.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.

关 键 词：Euler equations of isentropic gas dynamics zero-pressure flow transport equations Riemann problem delta shock wave vacuum flux approximation numerical simulations 

分 类 号：O354[理学—流体力学] TN103[理学—力学]