一种基于TV分裂的真正多维Riemann解法器

发布时间：2018-05-11 11:51

本文选题：Euler方程 + TV分裂　；参考：《应用数学和力学》2017年03期

【摘要】：给出了一种真正多维的HLL Riemann解法器.采用TV(Toro-Vázquez)分裂将通量分裂成对流通量和压力通量,其中对流通量的计算采用类似于AUSM格式的迎风方法,压力通量的计算采用波速基于压力系统特征值的HLL格式,并将HLL格式耗散项中的密度差用压力差代替,来克服传统的HLL格式不能分辨接触间断的缺点.为了实现数值格式真正多维的特性,分别计算网格界面中点和角点上的数值通量,并且采用Simpson公式加权中点和角点上的数值通量来得到网格界面上的数值通量.采用基于SDWLS(solution dependent weighted least squares)梯度的线性重构来获得空间的二阶精度,时间离散采用二阶Runge-Kutta格式.数值实验表明,相比于传统的一维HLL格式,该文的真正多维HLL格式具有能够分辨接触间断,消除慢行激波波后振荡以及更大的时间步长等优点.并且,与其他能够分辨接触间断的格式(例如HLLC格式)不同的是,真正多维的HLL格式在计算二维问题时不会出现数值激波不稳定现象.
[Abstract]:A real multidimensional HLL Riemann solver is presented. TV(Toro-V 谩 zquez splitting is used to split the flux into pair flux and pressure flux. The calculation of the flux is similar to the upwind method of the AUSM scheme, and the calculation of the pressure flux is based on the HLL scheme of wave velocity based on the eigenvalue of the pressure system. The density difference in the dissipative term of the HLL scheme is replaced by the pressure difference to overcome the shortcoming that the traditional HLL scheme can not distinguish the contact discontinuity. In order to realize the real multidimensional characteristics of the numerical scheme, the numerical fluxes at the midpoint and corner point of the grid interface are calculated, respectively, and the numerical flux on the grid interface is obtained by using the Simpson formula to weight the numerical flux on the midpoint and corner point. The linear reconstruction based on SDWLS(solution dependent weighted least squares) gradient is used to obtain the second order accuracy of space, and the second order Runge-Kutta scheme is used for time discretization. Numerical experiments show that compared with the traditional one-dimensional HLL scheme, the real multi-dimensional HLL scheme in this paper has the advantages of distinguishing contact discontinuities, eliminating the backward oscillations of slow-moving waves and increasing the time step. Moreover, unlike other schemes that can distinguish contact discontinuities (such as HLLC scheme), the real multidimensional HLL scheme does not exhibit numerical shock instability in the computation of two-dimensional problems.
【作者单位】：中国科学院数学与系统科学研究院计算数学与科学工程计算研究所;科学与工程计算国家重点实验室;
【基金】：国家重点基础研究发展计划(973计划)(2010CB731505) 国家自然科学基金(11321061);国家自然科学基金国际(地区)合作交流项目(NSFC-RGC11261160486)~~
【分类号】：O35

【相似文献】