A versatile conservative three-dimensional Cartesian cut-cell method for simulation of incompressible viscous flows over complex geometries is presented in this paper. The present method is based on the finite volume method on a non-uniform staggered grid together with a consistent mass and momentum flux computation. Contrary to the commonly cut-cell methods, an implicit time integration scheme is employed in the present method, which avoids numerical instability without any additional small cut-cell treatment. Strict conservation of the mass and momentum for both fluid and cut cells is enforced through the PISO algorithm for the pressure–velocity coupling. The versatility and robustness of the present cut-cell method are demonstrated by simulating various two- and three-dimensional canonical benchmarks (flow over a circular cylinder, airfoil, sphere, pipe, and heart sculpture) and the computed results agree well with previous experimental measurements and various numerical results obtained from the boundary-fitted, immersed boundary/interface, and other cut-cell methods, verifying the accuracy of the proposed method.

本文介绍了一种通用的保守三维笛卡尔切割单元方法，用于模拟复杂几何形状上的不可压缩粘性流动。本方法基于非均匀交错网格上的有限体积法以及一致的质量和动量通量计算。与常用的切割单元方法相反，本方法采用隐式时间积分方案，无需任何额外的小切割单元处理即可避免数值不稳定。流体和切割单元的质量和动量严格守恒通过压力-速度耦合的 PISO 算法强制执行。通过模拟各种二维和三维规范基准（流过圆柱体、翼型、