一种求解核函数方程的新方法—辅助核法

本文提出了求解核函数方程的辅助核法。此法克服了偶极子栅格法对网格分布的限制,具有更大的适用范围。数值计算表明,此法对求解绕翼型的跨声速激波流动是很有利的。

A NEW METHOD FOR SOLVING THE KERNAL EQUATIONS OF TRANSONIC FLOWS-AN AUXILIARY KERNAL METHOD

Solving the kernal equations is the key step in the integral equation method for transonic flows around airfoils (wings). The doublet lattice method is one of the main methods to solve the kernal equations, but it has a certain limitation on the distribution of mesh grids (usually uniform distribution) on the integral interval which is not convenient for its application to transonic flows with shocks as the great density of mesh points is necessary for accurate numerical solutions of the kernal equations.A new method for the solutions of the kernal equations-an auxiliary kernal method is proposed in the present paper which eliminates the limitation of the doublet lattice method on the distribution of mesh grids. So the method is suitable for solving the transonic flows with shocks.The method first turn the original kernal equations (a Fredlholm singular integral equation of the first kind) into a new kind of integral equations and then employs a numerical iterative algorithm to solve the resulting integral equations so as to obtain the solutions of the original kernal equations.Numerical calculations show that the auxiliary kernal method is more efficient than the doublet lattice method for transonic flows with shocks around airfoils.