高精度格式WCNS-E-5的Fourier分析与应用

High-Order Accurate Scheme WCNS-E-5 with Applications to two and Three-Dimensional Complicated Flows

对高精度加权紧致非线性格式WCNS-E-5进行了理论分析和应用研究。首先采用Fourier方法分析了WCNS-E-5与WCNS-5及其它高阶格式(迎风偏置格式EUW-5与标准格式)的差分误差特性,研究了它们在分辨效率方面的特性和相位误差在多维方向上的各向异性特性。分析结果显示WCNS-E-5与WCNS-5在色散与耗散特性方面优于EUW-5,分辨效率也普遍高于EUW-5和格式,而且它们的相位速度在多维方向上传播所表现的各向异性特性与其它高阶格式一致。WCNS-E-5的高精度特性与WCNS-5的一致,但在计算过程中少了三对角矩阵求解因而它的效率更高,于是采用WCNS-E-5数值模拟了二维/三维复杂流场,算例包括单涡斜向运动、二维Rie-mann问题以及存在分离的大攻角钝锥流动问题。计算结果体现了WCNS-E-5具有很低的数值耗散误差,它对激波、膨胀波和接触面等间断具有很好的捕捉能力,得到的图像清晰光滑,准确再现了真实流动现象。

The Fourier analysis of WCNS-E-5 with applications to complex flows is carried out,the difference errors of fifth-order WCNS(Weighted Compact Nonlinear Schemes) including WCNS-5 and WCNS-E-5 and other HOS(High-Order accurate Schemes) such as EUW-5(Explicit UpWind biased fifth-order scheme) and standard scheme are analyzed and their resolving efficiency as well as phase speed anisotropy are also discnssed. The analytical results show that WCNS outper forms EUW-5 in terms of dispersive and dissipative errors with higher resolving efficiency. The numerical tests including vortex evolution problem,two-dimensional Riemann problem and blunt cone flow at a large attack angle verify the strong robustness of WCNS-E-5 in capturing the discon tinuities of shock wave,rarefaction wave and contact surface. When similar grids are adopted in three-dimensional flows,more reliable and accurate heat flux with WCNS-E-5 is able to achieved than that with second-order schemes.