This paper presents a three-dimensional nonhydrostatic model to solve the Navier–Stokes equations using an unstructured finite volume method. The physical domain could be geometrically arbitrary. To avoid the checkerboard problem caused by non-staggered grids, a momentum interpolation method is used by introducing face-normal velocities at the mid-points of the cell faces. As the Large Eddy Simulation (LES) requires at least second-order accuracy in time and in space for all the terms, a central scheme combined with an explicit Adams–Bashforth scheme is proposed in this model. The projection method is applied to decouple the velocity field and pressure. Several benchmark test cases are used to validate the second-order accuracy, the numerical stability and the performance of the model. Analysis on divergence noise using an unstructured collocated triangular grid, as well as on the ratio between vertical and horizontal spacing steps have been done to show the reliability of the model. The proposed model has been used to simulate backward-facing step flows, lid-cavity flows, turbulent open channel flows and the turbulent flows around a vertical cylinder. The convergence of the linear solver is analyzed in terms of the iterations and CPU time. The results are fairly in agreement with the references in the literature. The proposed model is able to correctly reproduce the characteristic flow features in all the test cases.

本文提出了一个三维非静水模型，以非结构化有限体积法求解Navier-Stokes方程。物理域在几何上可以是任意的。为了避免由非交错网格引起的棋盘问题，通过在单元格面的中点引入面法线速度来使用动量插值方法。由于大涡模拟（LES）要求所有条件在时间和空间上至少具有二阶精度，因此在该模型中提出了结合显式Adams–Bashforth方案的中央方案。应用投影方法将速度场和压力解耦。使用几个基准测试用例来验证二阶准确性，数值稳定性和模型的性能。使用非结构化并置三角网格对发散噪声以及垂直和水平间距步长之比进行了分析，以显示模型的可靠性。所提出的模型已用于模拟向后的阶跃流，盖腔流，湍流明渠流和垂直圆柱体周围的湍流。根据迭代次数和CPU时间来分析线性求解器的收敛性。结果与文献中的参考文献完全一致。所提出的模型能够在所有测试案例中正确地再现特征流特征。盖腔流动，湍流开放通道流动以及湍流围绕垂直圆柱体流动。根据迭代次数和CPU时间来分析线性求解器的收敛性。结果与文献中的参考文献完全一致。所提出的模型能够在所有测试案例中正确地再现特征流特征。盖腔流动，湍流开放通道流动以及湍流围绕垂直圆柱体流动。根据迭代次数和CPU时间来分析线性求解器的收敛性。结果与文献中的参考文献完全一致。所提出的模型能够在所有测试案例中正确地再现特征流特征。