Two-Stage Fourth-Order Accurate Time Discretizations for 1D and 2D Special Relativistic Hydrodynamics (Journal of Computational Mathematics, 2020)
This paper studies the two-stage fourth-order accurate time discretization [J.Q. Li andZ.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-orderaccurate time discretizations can be proposed. With the aid of the direct Eulerian GRP(generalized Riemann problem) methods and the analytical resolution of the local "quasi1D" 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 ourschemes.