摘要
This paper studies the two-stage fourth-order accurate time discretization[J.Q.Li and Z.F.Du,SIAM J.Sci.Comput.,38(2016)]and its application to the special relativistic hydrodynamical equations.Our analysis reveals that the new two-stage fourth-order accurate time discretizations can be proposed.With the aid of the direct Eulerian GRP(generalized Riemann problem)methods and the analytical resolution of the local“quasi 1D”GRP,the two-stage fourth-order accurate time discretizations are successfully implemented for the 1D and 2D special relativistic hydrodynamical equations.Several numerical experiments demonstrate the performance and accuracy as well as robustness of our schemes.
基金
The authors were partially supported by the Special Project on High-performance Computing under the National Key R&D Program(No.2016YF B0200603)
Sci-ence Challenge Project(No.JCK Y2016212A502)
the National Natural Science Foundation of China(Nos.91630310&11421101).
