高超音速热流数值计算中的误差匹配原则

通过对粘性边界层的数值模拟和误差分析,提出了差分格式的误差匹配原则.在边界层内的计算网格一般都具有很大的长宽比,而计算误差与网格长宽比密切相关.为了使不同坐标方向上的误差保持在同一量级上,需根据误差匹配原则确定计算网格的尺寸.对绕钝锥的高超音速流动进行了数值模拟,进而计算了钝锥表面的热流分布.数值计算表明,参照误差匹配原则进行网格划分是有益的,可在保持流场数值计算精度和提高热流计算准确性的同时,使网格的数量和分布更为合理.

Error matching principle for heat transfer calculations in hypersonic flow simulations

An error matching principle, which is base on the error analysis of the computations with high-aspect-ratio grids, is derived for the finite difference simulation of the viscous boundary layer flows. The high- aspect-ratio grids were commonly used in numerical simulations of the viscous boundary layer flows and the main calculation error was always correlated to the aspect ratio of the grids. The principle above could be used to keep the same degree of the calculation error in spatial directions respectively. The error matching principle given was verified by the numerical simulation of the hypersonic flows over a blunt-cone. The flow field and the surface heat transfer rate were calculated in the numerical simulation. The results show that the error matching principle is great benefit to generate optimal grids. The optimal grids followed the error matching principle can minimize the error and improve the computational efficiency. At the same time, the accurate calculation of flow field and the surface heat transfer rate are benefited from the match of errors.