This paper develops the genuinely multidimensional HLL Riemann solver for the two-dimensional special relativistic hydrodynamic equations on Cartesian meshes and studies its physical-constraint preserving (PCP) property. Based on the resulting HLL solver, the first- and high-order accurate PCP finite volume schemes are proposed. In the high-order scheme, the WENO reconstruction, the third-order accurate strong-stability-preserving time discretizations and the PCP flux limiter are used. Several numerical results are given to demonstrate the accuracy, performance and resolution of the shock waves etc. as well as the genuinely multi-dimensional wave structures of our PCP finite volume schemes.

翻译：本文针对笛卡尔网格上的二维狭义相对论流体力学方程组，发展了真正多维的HLL黎曼求解器，并研究了其物理约束保持（PCP）性质。基于所得到的HLL求解器，提出了分别具有一阶和高阶精度的PCP有限体积格式。在高阶格式中，采用了WENO重构、三阶精度强稳定性保持时间离散以及PCP通量限制器。数值结果展示了我们的PCP有限体积格式在精度、性能、激波分辨率等方面的表现，以及其真正多维的波结构特征。