一种基于欧拉方程通量分裂的五阶有限差分共权多分辨率WENO格式  

A FIFTH-ORDER FINITE DIFFERENCE COMMON-WEIGHTS MULTI-RESOLUTION WENO SCHEME BASED ON THE FLUX VECTOR SPLITTING FOR EULER EQUATIONS

作　　者：张学莹 吴杨炯 ZHANG Xue-ying;WU Yang-jiong(School of Mathematics,Hohai University,Nanjing 210098,China)

机构地区：[1]河海大学数学学院,江苏南京211100

出　　处：《数学杂志》2024年第1期73-83,共11页Journal of Mathematics

基　　金：河海大学2023年新工科、新农科、新文科研究与改革实践项目资助(B2301914);河海大学2023年研究生“课程思政”示范课程建设项目资助(421203160)。

摘　　要：本文研究了欧拉方程的高精度数值解法,在多分辨率WENO数值格式中引入了共权思想,获得了一种新的五阶有限差分共权多分辨率WENO格式.数值实验表明,该方法在解的光滑区域能获得一致的高精度,在强间断附近能保持数值解基本无振荡的性质,从而验证算法的有效性.This article studies the high-precision numerical solution of Euler equations and introduces the common-weights idea into the multi-resolution WENO numerical scheme,obtaining a new fth-order nite di erence common-weights multi-resolution WENO scheme.Numerical experiments have shown that this method can achieve consistent high accuracy in the smooth region of the solution and maintain the essentially oscillatory nature of the numerical solution near strong discontinuities,thus verifying the e ectiveness of the algorithm.

关 键 词：欧拉方程 多分辨率WENO格式 共权 

分 类 号：O241.82[理学—计算数学]