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

• 作者: Huazhong Tang Yuhuan Yuan
• 来源期刊: 计算数学（英文版）
• 年，卷（期）: 2020,（5）
• 页码范围: 768-796
• 页数: 29页
• 语种: 英文
• DOI: 10.4208/jcm.1905-m2018-0020

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.