In this paper, We show for isentropic equations of gas dynamics with adiabatic exponent gamma=3 that approximations of weak solutions generated by large time step Godunov's scheme or Glimm's scheme give entrop...In this paper, We show for isentropic equations of gas dynamics with adiabatic exponent gamma=3 that approximations of weak solutions generated by large time step Godunov's scheme or Glimm's scheme give entropy solution in the limit if Courant number is less than or equal to 1.展开更多
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 f...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.展开更多
基金Supported in part by the National Natural Science of China, NSF Grant No. DMS-8657319.
文摘In this paper, We show for isentropic equations of gas dynamics with adiabatic exponent gamma=3 that approximations of weak solutions generated by large time step Godunov's scheme or Glimm's scheme give entropy solution in the limit if Courant number is less than or equal to 1.
基金supported by National Natural Science Foundation of China(Grant No.11361073)
文摘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.
