分辨率优化的混合WENO格式  

A Hybrid WENO Scheme for Resolution Optimization

作　　者：郭元 田奇 梁贤 李新亮 GUO Yuan;TIAN Qi;LIANG Xian;LI Xinliang(School of Mathematics and Information Science,Beifang University for Nationalities,Yinchuan 750021,China;School of Engineering Science,University of Chinese Academy of Sciences,Beijing 100049,China;State Key Laboratory of High Temperature Gas Dynamics,Institute of Mechanics,Chinese Academy of Sciences,Beijing 100190,China)

机构地区：[1]北方民族大学数学与信息科学学院,宁夏银川750021 [2]中国科学院大学工程科学学院,北京100049 [3]中国科学院力学研究所高温气体动力学国家重点实验室,北京100190

出　　处：《计算物理》2018年第4期397-404,共8页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(11472010,91441103,11372330,11472278);国家重点研发计划(2016YFA0401200);民用飞机专项科研(MJ-2015-F-028);科学挑战专题项目(JCKY2016212A501)资助

摘　　要：为提高有限差分格式的分辨率,利用傅里叶分析对WENO格式进行色散及耗散优化,并给出优化的线性权重.用优化后的WENO格式与保单调格式（MP）进行加权混合,得到新的加权混合WENO格式（H-WENO）.通过一维激波管问题、Shu-Osher问题及二维双Mach反射问题及R-T不稳定性问题对格式进行数值测试.结果显示,新格式具有强健的激波捕捉能力和对小尺度波结构的高分辨率,与原WENO格式相比改进明显.To improve finite difference scheme,Fourier analysis is used to optimize dispersion and dissipation of WENO scheme.And optimal linear weights are given. A class of hybrid schemes is designed by combing optimized WENO schemes with monotonicitypreserving scheme. A weighted hybrid WENO scheme（ H-WENO） is obtained. The scheme is tested with one-dimensional shock tube problem,Shu-Osher problem,two-dimensional Mach reflection problem and R-T instability problem. It shows that the scheme has strong ability to capture shock wave and high resolution for small scale wave structure,which is improved obviously compared with original WENO scheme.

关 键 词：混合格式 数值耗散 色散 保单调 优化 

分 类 号：O354.5[理学—流体力学]