TWO-STAGE FOURTH-ORDER ACCURATE TIME DISCRETIZATIONS FOR 1D AND 2D SPECIAL RELATIVISTIC HYDRODYNAMICS  

作　　者：Yuhuan Yuan Huazhong Tang 

机构地区：[1]Center for Applied Physics and Technology,HEDPS,and LMAM,School of Mathematical Sciences,Peking University,Beijing 100871,China

出　　处：《Journal of Computational Mathematics》2020年第5期768-796,共29页计算数学（英文）

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).

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.

关 键 词：Time discretization Shock-capturing scheme GRP method Relativistic hydrodynamics Hyperbolic conservation laws 

分 类 号：O17[理学—数学]