The numerical modelling of convection dominated high density ratio two-phase flow poses several challenges, amongst which is resolving the relatively thin shear layer at the interface. To this end we propose a sharp discretisation of the two-velocity model of the two-phase Navier-Stokes equations. This results in the ability to model the shear layer, rather than resolving it, by allowing for a velocity discontinuity in the direction(s) tangential to the interface. In a previous paper (Remmerswaal and Veldman (2022), arXiv:2209.14934) we have discussed the transport of mass and momentum, where the two fluids were not yet coupled. In this paper an implicit coupling of the two fluids is proposed, which imposes continuity of the velocity field in the interface normal direction. The coupling is included in the pressure Poisson problem, and is discretised using a multidimensional generalisation of the ghost fluid method. Furthermore, a discretisation of the diffusive forces is proposed, which leads to recovering the continuous one-velocity solution as the interface shear layer is resolved. The proposed two-velocity formulation is validated and compared to our one-velocity formulation, where we consider a multitude of two-phase flow problems. It is demonstrated that the proposed two-velocity model is able to consistently, and sharply, approximate solutions to the inviscid Euler equations, where velocity discontinuities appear analytically as well. Furthermore, the proposed two-velocity model is shown to accurately model the interface shear layer in viscous problems, and it is successfully applied to the simulation of breaking waves where the model was used to sharply capture free surface instabilities.
翻译:平流层以高密度比率为主的双相流的数值建模存在若干挑战,其中之一是解决界面中相对薄的剪剪层。 为此,我们建议对两相纳维埃-斯托克方程式的双速度模型进行清晰分解。 这使得能够模拟剪切层, 而不是解决它, 允许在方向向正向向向向向向移动速度不连续。 在上一份论文( Remmerswaal和Veldman (2022), Arxiv:22009.14934) 中, 我们讨论了质量和动力的运输, 其中两种液体尚未相互交错。 在本文中, 提议对两种液体进行隐含的联结, 使速度在界面正常方向上保持连续性。 组合包括在压力 Poisson 问题中, 并且通过对幽流模型的多维度方法进行分解。 此外, 提出分解的电流力力, 导致恢复一个速度的连续的解决方案, 在模型中, 直径直流中, 快速的电流与直径直流 。