In this paper, a second-order accurate method was developed for calculating fluid flows in complex geometries. This method uses cut-Cartesian cell mesh in finite volume framework. Calculus is employed to relate fluxes and gradients along curved surfaces to cell-averaged values. The resultant finite difference equations are sparse diagonal systems of equations. This method does not need repeated polynomial interpolation or reconstruction. Two-dimensional incompressible lid-driven semi-circular cavity flow at two Reynolds numbers was simulated with the current method and second-order accuracy was reached. The current method might be extended to third-order accuracy.

翻译：本文提出了一种用于计算复杂几何区域内流体流动的二阶精度方法。该方法在有限体积框架内采用切割笛卡尔网格，通过微积分将沿弯曲表面的通量与梯度关联为单元平均值。所得有限差分方程为稀疏对角方程组，无需重复的多项式插值或重构。利用该方法模拟了两种雷诺数下的二维不可压缩顶盖驱动半圆形空腔流动，并实现了二阶精度。该方法可拓展至三阶精度。