特定条件下高阶WENO格式计算结果误差  

Numerical errors of high-order WENO schemes under specific conditions

作　　者：刘君[1] 韩芳 魏雁昕 LIU Jun;HAN Fang;WEI Yanxin(School of Aeronautics and Astronautics,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]大连理工大学航天航空学院,大连116024

出　　处：《航空学报》2022年第2期225-234,共10页Acta Aeronautica et Astronautica Sinica

基　　金：国家重点研发计划(2018YFB0204404);国家自然科学基金(11872144)。

摘　　要：通过比较一阶迎风格式和五阶WENO格式模拟激波、接触间断、曲线坐标系下的均匀流和激波正规反射等4个简单流场得到的数值结果,发现WENO格式模拟的激波和接触间断在从初始间断变化成数值过渡区的过程中出现的非物理波动比一阶迎风格式的结果更加明显,流场结构也更加复杂;同时,由坐标变换而产生的几何诱导误差和边界近似模型误差也明显比一阶迎风格式的误差大。对这些现象进行数值和理论分析,得出高阶WENO格式在某些计算条件下存在放大计算结果误差的风险。受近期国内外文献启发,对目前高精度格式的空间多点构造方法和双曲型方程的特征线理论之间存在的矛盾进行了讨论。This paper compares the numerical results obtained from simulation of moving shock discontinuity,contact discontinuity,uniform flow in the curvilinear coordinate system and shock regular reflection in the first-order upwind scheme and the fifth-order WENO schemes.The shock and contact discontinuities simulated in the WENO schemes exhibit more pronounced non-physical fluctuations and more complicated flow field structures while changing from the initial discontinuity to the numerical transition region than the results in the first-order upwind scheme.Furthermore,the geometrically induced errors and boundary approximation model errors caused by coordinate transformations are significantly larger than those in the first-order upwind scheme.Numerical and theoretical analyses of the phenomena above conclude that higher-order WENO schemes run the risk of magnifying errors in the results under certain computational conditions.Finally,inspired by recently published articles,this paper discusses the contradiction between the current spatial multi-point construction method in high-order schemes and the characteristic line theory of hyperbolic equations.

关 键 词：有限差分法 高阶WENO格式 几何诱导误差 边界近似模型误差 双曲型方程 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]