A new numerical method is developed for the robust simulation of high-Reynolds number two-fluid flows with high density contrast. The proposed method is a combination of the consistent mass–momentum transport framework of Nangia et al. (J. Comput. Phys., 2019, 390: 548–594) and the coupled level-set and volume-of-fluid method of Sussman and Puckett (J. Comput. Phys., 2000, 162: 301–337). The conservative form of the momentum equation is solved, and the convection equation of density is solved together with the momentum equation at all cell faces. Moreover, consistent spatial and temporal discretization schemes are used to advance the governing equations of density and momentum to ensure a stable simulation. In the proposed method, the diffusion of the density or viscosity around the interface is not needed. In the test of a canonical case, the convection of a high density droplet, the proposed method makes an accurate prediction of the interface dynamics with a relatively low grid resolution. This feature is useful for reducing the computational cost for two-fluid flows with complex interface geometries. Furthermore, the test results show that the simulation is also stable for high Reynolds number two-fluid flows. In the case of wave breaking, the proposed method is stable for a high Reynolds number of $Re={10}^8$. In the test case of a collapsing and impinging water column, the present method makes good predictions on the water height and pressure that agree well with experimental results.

开发了一种新的数值方法，用于高密度对比的高雷诺数二流体流动的鲁棒仿真。所提出的方法是Nangia等人一致的质量动量运输框架的组合。（J. Comput。Phys 。，2019，390：548–594）以及Sussman和Puckett耦合的水平集和流体体积方法（J. Comput。Phys。，2000，162：301-337）。求解了动量方程的保守形式，并求解了所有单元面上的密度对流方程和动量方程。此外，使用一致的时空离散方案来推进密度和动量的控制方程，以确保稳定的仿真。在提出的方法中，不需要界面周围的密度或粘度的扩散。在对典型情况的测试中，即高密度液滴的对流，所提出的方法以相对较低的网格分辨率对界面动力学进行了准确的预测。此功能对于减少具有复杂接口几何形状的双流体流的计算成本很有用。此外，测试结果表明，该模拟对于高雷诺数二流体流动也是稳定的。在波浪破碎的情况下，所提出的方法对于较高的雷诺数是稳定的。$\mathrm{[R}Ë={10}^8$。在水柱坍塌和撞击的测试情况下，本方法对水的高度和压力做出了很好的预测，与实验结果吻合良好。