二维可压粘流N-S方程的边界元解法

THE APPLICATION OF BOUNDARY ELEMENT METHOD TO SOLVING COMPRESSIBLE N-S EQUATIONS

本文给出了一种求解二维可压Navier-Stokes(简称N-S)方程的边界元法。使用线化技术把控制方程变成变系数的线性偏微分方程,其基本解由组合代数的方法构造,从而给出了N-S方程的积分表达式。本文计算了几例低R_e数的跨声速翼型绕流,结果表明边界元法可以应用到可压粘流中。

The Boundary Element Method (BEM) or the Boundary Integral Equation Method (BIEM ) for solving two-dimen sional compressible Navier Stokes equations is presented in this paper. By using the linearization techniques, the equations are reduced to linear partial differential equations with variable coefficients. The fundamental solutions of these equations arc constructed by using an algebraic method based on the composition product of tensor products of kernel-distributions. By which the integral representations for the Navier-Stokes equations are finally established . Several numerical experiments for transonic viscous flows at low Reynolds numbers have been carried out to explore the capability of BEM to compressible viscous flows.