论文标题
使用耦合的Cahn-Hilliard / Navier-Stokes型号的雷利 - 泰勒不稳定性的二维和三维模拟
Two- and Three-Dimensional Simulations of Rayleigh-Taylor Instabilities Using a Coupled Cahn-Hilliard / Navier-Stokes Model
论文作者
论文摘要
我们报告了不混溶的液体中雷利 - 泰勒不稳定性的二维数值模拟。使用Cahn-Hilliard方程组合，管理一个流体的体积分数的演变以及管理散装速度和压力的Navier-Stokes方程的漫射界面模型。由于使用BousSinesQ近似，该研究仅限于低atwood数。该代码基于伪谱法。首先在瑞利 - 泰勒不稳定性的二维情况下进行线性分析，以确认该模型在Inviscid或粘性流体的情况下很好地捕获了这种现象。这项工作的一个关键方面是，定量研究了与Cahn-Hilliard方程（界面厚度和迁移率）相关的热力学参数的影响。然后呈现粘性流体中雷利 - 泰勒不稳定性的三维结果，以显示该建模的可能性。我们观察到粘度和初始单模式扰动的粘度和波长对非线性状态期间质量传输的影响。
We report on two- and three-dimensional numerical simulations of Rayleigh-Taylor instabilities in immiscible fluids. A diffuse-interface model that combines the Cahn-Hilliard equation, governing the evolution of the volume fraction of one fluid, and the Navier-Stokes equations, governing the bulk velocity and pressure, is used. The study is limited to low Atwood numbers owing to the use of the Boussinesq approximation. The code is based on a pseudo-spectral method. A linear analysis is first performed in a two-dimensional case of Rayleigh-Taylor instability to confirm that the model very well captures this phenomenon in the case of inviscid or viscid fluids. One key aspect of this work is that the influence of the thermodynamic parameters related to the Cahn-Hilliard equation (interface thickness and mobility) is quantitively studied. Three-dimensional results of Rayleigh-Taylor instabilities in viscous fluids are then presented to show the possibilities of this modeling. We observe the effect of the viscosity and the wavelength of an initial single-mode perturbation on the mass transport during the nonlinear regime.
