几个求解Euler方程的验证模型  

Several Models for Verificating Numerical Solution of Euler Equation

作　　者：刘君 刘瑜 LIU Jun;LIU Yu(Faculty of Mechanical Engineering&Mechanics,Ningbo University,Ningbo 315211,China)

机构地区：[1]宁波大学机械与力学学院,浙江宁波315211

出　　处：《气体物理》2024年第6期62-73,共12页Physics of Gases

基　　金：宁波市科技创新2025重大项目(2022Z186)。

摘　　要：从2018年开始陆续发现在特定条件下WENO格式计算误差比1阶迎风格式还大的数值算例。经过定性分析后,作者认为这种现象是采用空间多点模板构造格式的方法不符合双曲型方程的特征线理论以及通量分裂格式引入非物理波动所致。提出了基于Euler方程对1阶迎风、MUSCL和WENO格式进行各种比对数值实验论证这个观点的若干算例。希望将其作为差分法求解Euler方程的验证模型,以供同行参考。目前国内外文献中验证高阶格式的经典算例,例如等熵涡、双Mach反射、激波和自由界面干扰等,验证时大多根据数值现象定性比较,缺乏定量指标,本文提出的验证模型能够计算数值解误差,可以进行定量评价。通过对这些验证模型的分析,提出了一种可以有效降低初始激波诱导误差的算法。The authors have successively found numerical examples in which the computational error of the WENO is larger than that of the first-order upwinding scheme under specific conditions since 2018.After qualitative analyses,the authors attribute this phenomenon to the fact that the method of constructing the scheme using a spatial multipoint stencil does not comply with the characteristic theory of hyperbolic equation as well as the introduction of unphysical fluctuations in the flux splitting scheme.This paper was a collection of examples from various comparative numerical experiments conducted over the years based on the Euler equations for the first-order upwinding,MUSCL,and WENO schemes to demonstrate this point of view.It is hoped that it will be used as a verification model for solving Euler equations by the finite difference method for the reference of colleagues.Currently,the classical examples of verification of higher-order schemes in domestic and inter-national literature,such as isentropic vortices,double Mach reflections,shock waves and free-interface interactions,etc.,are mostly verified based on the qualitative comparison of numerical phenomena and lack of quantitative indicators.The verifi-cation model in this paper is able to calculate the numerical error,which can be evaluated quantitatively.By analyzing these validation models,an algorithm was proposed that can effectively reduce the induced error of the initial shock wave.

关 键 词：验证 高阶格式 加权本质无振荡格式 几何守恒律 通矢量分裂 通量差分分裂 

分 类 号：O355[理学—流体力学] V211[理学—力学]