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.
Keywords: Time discretization; Shock-capturing scheme; GRP method; Relativistic hydrodynamics; Hyperbolic conservation laws.