相对论流体力学方程的高分辨率熵相容格式  

High Resolution Entropy Consistent Scheme for Relativistic Hydrodynamics Equations

作　　者：高凡琪 封建湖[1] 郑素佩[1] 任璇 

机构地区：[1]长安大学理学院,陕西 西安 [2]西北工业大学航天学院,陕西 西安

出　　处：《应用数学进展》2022年第12期8691-8703,共13页Advances in Applied Mathematics

摘　　要：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.

关 键 词：相对论流体力学方程 斜率限制器 高分辨率 熵相容格式 

分 类 号：O241.8[理学—计算数学]