Two-stage fourth-order accurate time discretizations for 1D and 2D special relativistic hydrodynamics

Abstract

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.

27 pages

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Cited by in corpus (6)

• Entropy stable adaptive moving mesh schemes for 2D and 3D special relativistic hydrodynamics
• High-order accurate entropy stable nodal discontinuous Galerkin schemes for the ideal special relativistic magnetohydrodynamics
• High-order accurate entropy stable adaptive moving mesh finite difference schemes for special relativistic (magneto)hydrodynamics
• Second-order accurate BGK schemes for the special relativistic hydrodynamics with the Synge equation of state
• On the explicit two-stage fourth-order accurate time discretizations
• A physical-constraints-preserving genuinely multidimensional HLL scheme for the special relativistic hydrodynamics