A new finite element method, the Least-Based Operator-Splitting (LSBOS) algorithm, was developed to solve N-S equations. At each time interval, the equations are split into a diffusion term and a convection term by adopting the operator-splitting algorithm. For the diffusion term, the temporal discretization is performed with the backward difference method and the spatial discretization is performed with the standard Galerkin method, For the convection term, the temporal discretization is also performed with the backward difference method and the spatial discretization is performed with the least square scheme. The driven square flow and the backward-facing step flow are replicated with this algorithm. The computed results agree with the standard solution for the simulations of driven square flow. For the simulations of the backward-facing step flow, the flow field characteristics and the velocity distributions also agree with the experimental data using different Reynolds numbers. These comparisons indicate that the LSBOS algorithm has good convergence and high accuracy.%提出一种新的求解N-S方程的有限元法,即基于最小二乘的N-S方程算子分裂有限元法.该算法采用算子分裂法将N-S方程分解成扩散项和对流项:扩散项时间离散采用向后差分格式,空间离散采用标准Galerkin有限元法；对流项时间离散采用向后差分格式,空间离散采用最小二乘有限元法.应用该算法对方腔流和后台阶流进行数值模拟,方腔流数值计算结果与标准解吻合很好；在后台阶流数值模拟中给出了不同雷诺数下的流场特征和速度对比曲线,所得计算结果与试验结果吻合较好,表明基于最小二乘的N-S方程算子分裂有限元法具有较好的收敛性和较高的精度.
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