A Third-Order Accurate Direct Eulerian GRP Scheme for One-Dimensional Relativistic Hydrodynamics. Issue 2 (May 2014)

• Record Type: Journal Article
• Authors: Wu, Kailiang; Yang, Zhicheng; Tang, Huazhong
• Is Part Of: East Asian journal on applied mathematics. Volume 4:Issue 2(2014)
• Page Start: 95
• Page End: 131
• Publication Date: 2014-05
• Subjects: 65M06, -- 76M12, -- 76Y05; Godunov-type scheme, -- WENO, -- generalised Riemann problem, -- Riemann invariant, -- Rankine-Hugoniot jump condition, -- relativistic hydrodynamics; Applied mathematics -- Periodicals; 519.05
• DOI: 10.4208/eajam.101013.100314a
• Languages: English
• ISSNs: 2079-7362

Abstract

Abstract: A third-order accurate direct Eulerian generalised Riemann problem (GRP) scheme is derived for the one-dimensional special relativistic hydrodynamical equations. In our GRP scheme, the higher-order WENO initial reconstruction is employed, and the local GRPs in the Eulerian formulation are directly and analytically resolved to third-order accuracy via the Riemann invariants and Rankine-Hugoniot jump conditions, to get the approximate states in numerical fluxes. Unlike a previous second-order accurate GRP scheme, for the non-sonic case the limiting values of the second-order time derivatives of the fluid variables at the singular point are also needed for the calculation of the approximate states; while for the sonic case, special attention is paid because the calculation of the second-order time derivatives at the sonic point is difficult. Several numerical examples are given to demonstrate the accuracy and effectiveness of our GRP scheme.