Two-stage fourth-order accurate time discretizations for 1D and 2D special relativistic hydrodynamics
This work provides a high-order accurate numerical method for solving special relativistic hydrodynamics, which is important for astrophysical simulations, but the approach is an incremental extension of existing techniques.
This paper develops two-stage fourth-order accurate time discretizations for 1D and 2D special relativistic hydrodynamical equations, implementing them with direct Eulerian GRP methods. Numerical experiments demonstrate the schemes' performance, accuracy, and robustness.
This paper studies the two-stage fourth-order accurate time discretization \cite{LI-DU:2016} and applies it to special relativistic hydrodynamical equations. It is shown that new two-stage fourth-order accurate time discretizations can be proposed. With the aid of the direct Eulerian GRP (generalized Riemann problem) methods \cite{Yang-He-Tang:2011,Yang-Tang:2012} 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.