In this work, Free Element method (FECM) is extended to solve incompressible Navier‐Stokes equations. The momentum equations are discretized by FECM, which permits overlapped elements. Then, the velocities at midpoints are interpolated by improved Momentum Interpolation Method to avoid oscillation caused by decoupling of velocity and pressure. At last, the pressure correction equation is solved to make sure the results satisfying continuity equation. The interpolation of midpoint's velocity is proved to be independent of the under‐relaxation factor and time step size. The deferred correction is employed for utilization of higher‐order discretization of convective terms. Taylor‐Green vortex, flow over a cylinder, lid‐driven flow, cooling tunnel, and flow over airfoil are simulated. The results computed by the proposed method are compared with exact solutions and benchmark solutions, which indicates that the new method has the second order accuracy in space. What is more, the proposed method works well on random node distributions as well, which means that the method is much robust.

中文翻译：

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用于模拟二维和三维不可压缩流体流动的自由元方案

在这项工作中，扩展了自由元素方法（FECM）来求解不可压缩的Navier-Stokes方程。动量方程由FECM离散化，从而允许元素重叠。然后，通过改进的动量插值方法对中点的速度进行插值，以避免由速度和压力的解耦引起的振荡。最后，求解压力校正方程，以确保结果满足连续性方程。事实证明，中点速度的插值与欠松弛因子和时间步长无关。递延校正用于对流项的高阶离散化。对泰勒-格林涡流，圆柱体上的流动，盖驱动的流动，冷却通道以及翼型上的流动进行了模拟。将该方法计算的结果与精确解和基准解进行了比较，表明该方法在空间上具有二阶精度。而且，所提出的方法在随机节点分布上也能很好地工作，这意味着该方法非常健壮。