Two-Stage Fourth-Order Accurate Time Discretizations for 1D and 2D Special Relativistic Hydrodynamics
Year: 2020
Author: Huazhong Tang, Yuhuan Yuan
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 5 : pp. 768–796
Abstract
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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1905-m2018-0020
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 5 : pp. 768–796
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Time discretization Shock-capturing scheme GRP method Relativistic hydrodynamics Hyperbolic conservation laws.