论文标题
一个尖锐的结构，可保留两相流的两速度模型
A sharp, structure preserving two-velocity model for two-phase flow
论文作者
论文摘要
对流的数值建模主导高密度比两相流动构成了几个挑战，其中包括解决界面处的相对较薄的剪切层。为此，我们提出了两相纳维尔 - 斯托克斯方程的两速度模型的急剧离散化。这可以通过允许在与接口的方向上的速度不连续性来对剪切层建模而不是解决剪切层的能力。 在上一篇论文（Remmerswaal and Veldman（2022），Arxiv：2209.14934）中，我们讨论了质量和动量的运输，其中两种流体尚未耦合。在本文中，提出了两种流体的隐式耦合，这在界面正常方向上施加了速度场的连续性。耦合包含在压力泊松问题中，并使用幽灵流体方法的多维概括进行离散化。此外，提出了扩散力的离散化，这会导致在解决界面剪切层时恢复连续的单速度解决方案。 提出的两速度公式经过验证，并将其与我们的单速度公式进行了比较，在那里我们考虑了许多两相流量问题。已经证明，所提出的两个速度模型能够始终如一，急剧地对Inviscid Euler方程的近似解决方案，其中速度不连续性也在分析上也是如此。此外，所提出的两速度模型被证明可以准确地对粘性问题进行剪切层建模，并成功地应用于模拟波动的模拟，其中使用该模型迅速捕获自由表面的稳定性。
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.
