Under consideration are the issues of numerical solution of a. boundary integral equation describing the vorticity generation process on the streamlined airfoils in meshless vortex methods. The traditional approach based on the quadrature method leads to the necessity of solving a. system of linear algebraic equations with dense matrix. If we consider the system of airfoils moving relative to one another, this procedure has to be performed at each time step of the calculation, and its high computational complexity significantly reduces the efficiency of vortex methods. The transition from the traditional approach expressed by an integral equation of the first kind to an approach with the integral equation of the second kind makes it possible to apply the simple-iteration method for numerical solving the boundary integral equation. By examples of some model problems, we demonstrate that the iterative approach allows reducing the computational complexity of the problem by tens to hundreds times while providing an acceptable accuracy of the approximate solution.

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计算流体力学二维涡旋方法中边界积分方程的迭代求解方法

正在考虑a的数值解的问题。边界积分方程，描述了无网格涡旋方法中流线型翼型上涡度产生过程。基于正交方法的传统方法导致解决a的必要性。稠密矩阵的线性代数方程组。如果我们考虑翼型系统相对运动的问题，则必须在计算的每个时间步执行此过程，并且其高计算复杂性显着降低了涡旋方法的效率。从由第一类积分方程表示的传统方法到具有第二类积分方程的方法的转变，使得可以将简单迭代方法用于数值求解边界积分方程。