二维粘性流动的边界元方法

Boundary Element Method of the 2 -D Viscous Fluid Flow

本文叙述了粘性流动边界元方法,并研究了动力润滑、涡旋发生以及生物力学等问题。该方法基于用Stokes方程的基本解作为格林函数,将N-S方程归结为求解区域边界上的积分方程,使用边界单元,数值求解积分方程。给出了应力分布、压力分布及速度场。数值结果与理论结果和实验结果十分符合,方法具有很高的精度,比起目前的差分法和有限元法,在某些问题上更有效,也更灵活。

In this paper, the Viscous Boundary Element Method (VBEM) was used to treat problems in theory of hydrodynamic lubrication, occurrence of vortex, and biomechanics. The method is based on the idea of taking the fundamental solution of Stokes equations as Green's function to convert the N-S equations to boundary integrel equations. The intergral equations are solved numerically. The stress and pressure distributions, and velocity fields are given. The numerical results are found to be consistent with theoretical ones and in excellent agreement with the experimental ones. The method is of higher accuracy, more efficient and more flexible in handling complex geometry than the existing finite difference method and finite element method.