涡量流函数法模拟方腔内粘性不可压流动

摘要

Combined iteration method was used to gain the analytical solution of two-dimensional square acvity flow by nondimensionalized derivation and discrete of vorticity equation. Based on Matlab programming, vortex stream function method solved two-dimensional square cavity flow. Finite volume method solved the conservation equations. QUICK scheme and two-order-central-difference scheme were applied into convection and diffusion terms separately. The delay correction technique of discrete format was applied into finite volume method for calculation. The distribution of each physical quantity was obtained when the flow is in a steady state.%通过对涡量控制方程进行无量纲化推导和离散,用联合迭代方法求解二维方腔流动这一不可压缩黏性典型流动的解析解.基于Matlab编程,采用涡量流函数法求解二维方腔流动,计算采用有限体积算法,对流项采用QUICK格式,扩散项采用二阶中心差分格式,并采用延迟修正技术的离散格式对该问题进行数值求解,得到流动达到稳定状态时各物理量的分布.