TY - JOUR
T1 - A Third-Order Accurate Direct Eulerian GRP Scheme for One-Dimensional Relativistic Hydrodynamics
AU - Kailiang Wu, Zhicheng Yang & Huazhong Tang
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 95
EP - 131
PY - 2018
DA - 2018/02
SN - 4
DO - http://doi.org/10.4208/eajam.101013.100314a
UR - https://global-sci.org/intro/article_detail/eajam/10825.html
KW - Godunov-type scheme, WENO, generalised Riemann problem, Riemann invariant, Rankine-Hugoniot jump condition, relativistic hydrodynamics.
AB - <p style="text-align: justify;">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.</p>