求解欧拉方程的嵌入WENO格式  

The Embedded WENO Scheme for Solving the Euler Equation

作　　者：白晓雅 郑秋亚[1] 梁益华[2] BAI Xiaoya;ZHENG Qiuya;LIANG Yihua(School of Science, Chang′an University, Xi′an 710064, China;Aeronautical Laboratory of Computational Fluid Dynamics, Aeronautics Computing Technique Research Institute, Xi′an 710068, China)

机构地区：[1]长安大学理学院,陕西西安710064 [2]中国航空计算技术研究所,航空气动力数值模拟重点实验室,陕西西安710068

出　　处：《郑州大学学报（理学版）》2020年第3期98-103,共6页Journal of Zhengzhou University:Natural Science Edition

基　　金：航空科学基金项目(2015ZA31002)。

摘　　要：为了优化欧拉方程数值计算,提出了五阶嵌入式加权本质无振荡(Embedded-WENO)格式耦合低耗散总能对流迎风和分压(E-CUSP)格式后所得的新格式E-CUSP-Embedded-WENO5。新格式在空间方向上对E-CUSP所得的通量采用Embedded-WENO格式重构,在时间方向上采用四阶保持强稳定龙格-库塔方法。使用新格式对欧拉方程进行数值模拟,结果表明,新格式在激波附近更接近理论解,稳定性更好且分辨率更高,对激波和接触间断的捕捉能力更强,尤其是对激波的捕捉仅需要两到三个单元。In order to optimize the numerical calculation of Euler equation,a new scheme(E-CUSP-Embedded-WENO5)was proposed,which was obtained by embedded weighted essential-no-oscillation(Embedded-WENO)scheme coupling low-dissipation total energy convection upwind and partial pressure(E-CUSP)scheme.In the new scheme,the flux obtained by E-CUSP was reconstructed by Embedded-WENO scheme in spatial direction and the fourth-order strong stable Runge-Kutta method in time direction.The results showed that the new scheme was closer to the theoretical solution near the shock wave.It also had better stability,higher resolution and stronger ability to capture shock wave and contact discontinuity,especially for capturing shock wave,only two to three elements were needed.

关 键 词：嵌入式加权本质无振荡格式 高分辨率 欧拉方程 龙格-库塔方法 

分 类 号：O242[理学—计算数学]