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相对论流体力学方程的高分辨率熵相容格式
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Abstract:
本文提出了一种求解相对论流体力学方程的高分辨率熵相容格式。新格式主要是由熵相容格式以及斜率限制器两个部分构成。首先设计了一个熵相容格式(EC格式)的数值通量。接着为了更好地捕捉到解的结构，建立了一个基于MUSCL (Monotone Upstream-centred Scheme for Conservation Laws)型重建方法的斜率限制器，并将它应用于熵相容格式中，从而得到了高分辨率熵相容格式(EC-Limited格式)。文中还证明了新构造的EC格式和EC-Limited格式的收敛性。在解的光滑区域，EC-Limited格式具有高精度的特性；而在解的间断区域，EC-Limited格式能够恰当地控制耗散，从而抑制非物理现象的发生。最后，对相对论流体力学方程的一维和二维算例进行数值模拟，证明了新格式的稳定性以及良好的性能。
A high-resolution entropy consistent scheme was developed for solving the relativistic hydrody-namics equations. The new scheme is composed of entropy consistent scheme and slope limiter. First, an entropy consistent numerical flux (EC scheme) was designed. In order to capture the struc-ture of the solution better, a slope limiter based on MUSCL (Monotone Upstream-centred Scheme for Conservation Laws) type reconstruction method is constructed, the high-resolution entropy con-sistent scheme is obtained by applying it to the entropy consistent scheme. The convergences of the EC scheme and EC-Limited scheme have been proved. For the smooth region of the solution, the EC-Limited scheme has the characteristics of high accuracy, and for the discontinuous region, it can precisely control the dissipation and restrain the occurrence of non-physical phenomena. Finally, several one and two-dimensional numerical experiments demonstrate the stability and good performance of the high-resolution entropy consistent scheme.
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