基于动理学的低耗散通量分裂格式  

Kinetic-theory-based low diffusion flux vector splitting scheme

作　　者：陈艺冰[1,2] 江松[1] 刘娜 

机构地区：[1]北京应用物理与计算数学研究所 [2]计算物理重点实验室 [3]中物院高性能数值模拟软件中心

出　　处：《中国科学：数学》2015年第8期1217-1230,共14页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11101047);中物院科学技术发展基金(批准号:2013A0202011)资助项目

摘　　要：通量分裂格式具有简单、稳健等特点而备受大型工程应用CFD软件青睐,但传统的通量分裂格式往往引入过多数值耗散,特别对于接触间断和稀疏波等区域难以给出令人满意的解.本文首先借鉴Toro-Vazquez通量分裂方法的思想,将控制方程的通量分裂成对流项和压力项,随后,采用基于通量分裂的动理学方法分别进行离散.其中对流项采用迎风型格式离散,从而提高了接触间断处的分辨率.压力项首先采用NOK(non-oscillation kinetic)格式进行离散,而后为了进一步提高格式精度增加了碰撞项,最终得到一种新的低耗散通量分裂格式(LDK格式).新算法不仅形式简单而且稳健,而且与传统通量分裂方法相比,在接触间断具有更高的分辨率,稀疏波具有更高精度.数值算例给出了新方法与目前多种常用数值算法的比较结果,证实了新方法的良好效果.Flux vector splitting （FVS） schemes are simple and robust. These two advantages are very attractive for large engineering application CFD softwares. However, traditional FVS schemes often introduce over diffusions and cannot give satisfied solutions for the contact discontinuities and rarefaction waves. In this article, following the idea of Toro-Vazquez, we firstly divide the flux into two parts： convective terms and pressure terms. Then the flux vector splitting kinetic scheme is used to construct the numerical scheme for both terms. Upwind scheme is chosen to discretize the convective terms to improve the resolution near the contact discontinuities. NOK scheme is utilized to discretize the pressure terms, and the collision terms are also added to improve the accuracy. Finally, a new low diffusion kinetic （LDK） flux vector splitting scheme is obtained. This new scheme is simple and robust, and has higher resolution near the contact discontinuities and higher accuracy near the rarefaction waves compared with the traditonal FVS. Numerical tests shows the comparisons between some current numerical schemes and the new scheme, and demonstrate that this new scheme behaves well in all the test cases.

关 键 词：可压缩流 通量分裂 低耗散 动理学 

分 类 号：O35[理学—流体力学]