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.