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Volume 38, Issue 5
Two-Stage Fourth-Order Accurate Time Discretizations for 1D and 2D Special Relativistic Hydrodynamics

Huazhong Tang & Yuhuan Yuan

DOI: 10.4208/jcm.1905-m2018-0020

J. Comp. Math., 38 (2020), pp. 768-796.

Published online: 2020-04

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  • 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.

  • Keywords

Time discretization, Shock-capturing scheme, GRP method, Relativistic hydrodynamics, Hyperbolic conservation laws.

  • AMS Subject Headings

65M08, 65M06, 76M12, 76M20, 76Y05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hztang@math.pku.edu.cn (Huazhong Tang)

1548602562@qq.com (Yuhuan Yuan)

  • BibTex
  • RIS
  • TXT
@Article{JCM-38-768, author = {Tang , Huazhong and Yuan , Yuhuan}, title = {Two-Stage Fourth-Order Accurate Time Discretizations for 1D and 2D Special Relativistic Hydrodynamics}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {5}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1905-m2018-0020}, url = {http://global-sci.org/intro/article_detail/jcm/16669.html} }
TY - JOUR T1 - Two-Stage Fourth-Order Accurate Time Discretizations for 1D and 2D Special Relativistic Hydrodynamics AU - Tang , Huazhong AU - Yuan , Yuhuan JO - Journal of Computational Mathematics VL - 5 SP - 768 EP - 796 PY - 2020 DA - 2020/04 SN - 38 DO - http://doi.org/10.4208/jcm.1905-m2018-0020 UR - https://global-sci.org/intro/article_detail/jcm/16669.html KW - Time discretization, Shock-capturing scheme, GRP method, Relativistic hydrodynamics, Hyperbolic conservation laws. AB -

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.

Tang , Huazhong and Yuan , Yuhuan. (2020). Two-Stage Fourth-Order Accurate Time Discretizations for 1D and 2D Special Relativistic Hydrodynamics. Journal of Computational Mathematics. 38 (5). 768-796. doi:10.4208/jcm.1905-m2018-0020
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