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
This paper develops the high-order accurate entropy stable finite difference schemes for one-and two-dimensional special relativistic hydrodynamic equations.The schemes are built on the entropy conservative flux and t...This paper develops the high-order accurate entropy stable finite difference schemes for one-and two-dimensional special relativistic hydrodynamic equations.The schemes are built on the entropy conservative flux and the weighted essentially non-oscillatory(WENO)technique as well as explicit Runge-Kutta time discretization.The key is to technically construct the affordable entropy conservative flux of the semi-discrete second-order accurate entropy conservative schemes satisfying the semi-discrete entropy equality for the found convex entropy pair.As soon as the entropy conservative flux is derived,the dissipation term can be added to give the semidiscrete entropy stable schemes satisfying the semi-discrete entropy inequality with the given convex entropy function.The WENO reconstruction for the scaled entropy variables and the high-order explicit Runge-Kutta time discretization are implemented to obtain the fully-discrete high-order entropy stable schemes.Several numerical tests are conducted to validate the accuracy and the ability to capture discontinuities of our entropy stable schemes.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 the Special Project on High-performance Computing under the National Key R&D Program(No.2016YFB0200603)Science Challenge Project(No.TZ2016002)the National Natural Science Foundation of China(Nos.91630310 and 11421101),and High-Performance Computing Platform of Peking University.
文摘This paper develops the high-order accurate entropy stable finite difference schemes for one-and two-dimensional special relativistic hydrodynamic equations.The schemes are built on the entropy conservative flux and the weighted essentially non-oscillatory(WENO)technique as well as explicit Runge-Kutta time discretization.The key is to technically construct the affordable entropy conservative flux of the semi-discrete second-order accurate entropy conservative schemes satisfying the semi-discrete entropy equality for the found convex entropy pair.As soon as the entropy conservative flux is derived,the dissipation term can be added to give the semidiscrete entropy stable schemes satisfying the semi-discrete entropy inequality with the given convex entropy function.The WENO reconstruction for the scaled entropy variables and the high-order explicit Runge-Kutta time discretization are implemented to obtain the fully-discrete high-order entropy stable schemes.Several numerical tests are conducted to validate the accuracy and the ability to capture discontinuities of our entropy stable schemes.
