@Article{EAJAM-4-95,
author = {},
title = {A Third-Order Accurate Direct Eulerian GRP Scheme for One-Dimensional Relativistic Hydrodynamics},
journal = {East Asian Journal on Applied Mathematics},
year = {2018},
volume = {4},
number = {2},
pages = {95--131},
abstract = {<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>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.101013.100314a},
url = {http://global-sci.org/intro/article_detail/eajam/10825.html}
}