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

Yuhuan Yuan, Huazhong Tang   

  1. Center for Applied Physics and Technology, HEDPS, and LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China
  • Received:2018-02-08 Revised:2019-03-03 Online:2020-09-15 Published:2021-03-11
  • Supported by:
    The authors were partially supported by the Special Project on Highperformance Computing under the National Key R&D Program (No. 2016YFB0200603), Science Challenge Project (No. JCKY2016212A502), and the National Natural Science Foundation of China (Nos. 91630310 & 11421101).

Yuhuan Yuan, Huazhong Tang. TWO-STAGE FOURTH-ORDER ACCURATE TIME DISCRETIZATIONS FOR 1D AND 2D SPECIAL RELATIVISTIC HYDRODYNAMICS[J]. Journal of Computational Mathematics, 2020, 38(5): 768-796.

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.

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