一种混合优化差分格式

优化差分格式一般用于计算气动声学和小尺度的湍流数值模拟，这类格式为了获取更好的短波分辨率通常牺牲了部分收敛精度.文章尝试结合最高阶精度格式与优化格式的特点，构造混合优化格式，提高优化格式的收敛精度以及谱分辨率.混合优化格式由模板上的最高阶精度格式与优化格式加权组合得到，权系数由当前模板上的值确定，这使得该格式为非线性格式.对于单色波问题，通过优化权的设计可大幅度减小相位误差.但是加权混合过程使得计算时间有所增加.数值计算证明了该格式的特点. 

A Hybrid Optimized Difference Scheme

The optimized difference scheme, which is applied for computational aeroacoustics(CAA) problems and direct numerical simulations(DNS) of compressible turbulent flows, is generally designed for better resolution on short waves. However, the accuracy order of the scheme is usually decreased in the optimization procedure. In this paper, a hybridization of the optimized scheme and the highest order scheme was proposed to improve the convergence accuracy and the spectral resolution. This is a weighted convex combination of the two schemes. The weight is determined by the value in the stencil and thus the final scheme is nonlinear. The phase error is reduced substantially for problems of monochromatic waves. But the computational cost is increased because of the weighted hybridization. Numerical tests validate the good property of the proposed scheme.