Second order approximation for a quasi-incompressible Navier-Stokes Cahn-Hilliard system of two-phase flows with variable density
Second order approximation for a quasi-incompressible Navier-Stokes Cahn-Hilliard system of two-phase flows with variable density
复制标题
变密度两相流准不可压缩纳维-斯托克斯卡恩-希利亚德系统的二阶近似
DOI：
10.1016/j.jcp.2021.110727
复制
发表时间：
2021-10-04
影响因子：
4.1
通讯作者：
Lowengrub, John
中科院分区：
文献类型：
--
作者：
Guo, Zhenlin;Cheng, Qing;Lowengrub, John
相场模型已广泛并成功地应用于模拟变密度的两相流。已经提出了几种稳定的数值方法来求解这种高度非线性和耦合的系统。关键问题是设计一种方法，使其能够在离散水平上保留（精确或稍微修改的）流体系统的能量守恒/耗散定律。然而，大多数现有的能量稳定数值方法对于不同密度的两相流仅限于时间上的一阶精度。变密度两相流的时间二阶精确数值方法的设计仍然具有挑战性。在本文中，我们为变密度两相流的准不可压缩纳维-斯托克斯卡恩-希利亚德模型开发了几个二阶、稳健且精确的数值方案，该模型在热力学上是一致的，最初是在[1]中开发的，用于模拟复杂几何形状的两相流。特别是，本文提出的数值格式可以保留质量守恒定律或能量耗散定律。提供了几个数值示例来验证我们数值方案的稳健性和准确性。(c) 2021 Elsevier Inc. 保留所有权利。
Phase-field model has been applied extensively and successfully for simulating two-phase flows with variable density. Several stable numerical methods have been proposed for solving such a highly nonlinear and coupled system. The key issue is to design a method such that it can preserve the (exact or slightly modified) conservative/dissipative law of energy of the fluid system at the discrete level. However, most of the existing energy stable numerical methods are restricted to only the first order accuracy in time for two-phase flow with different density. The design of a temporally second order accurate numerical method for the two-phase flows with variable density still remains challenging. In this paper, we develop several second order, robust and accurate numerical schemes for a quasi-incompressible Navier-Stokes Cahn-Hilliard model of two-phase flows with variable density which is thermodynamically consistent and was originally developed in [1] for simulating two-phase flows in complex geometries. Especially, numerical schemes proposed in this paper can preserve the mass conservation or energy dissipative law. Several numerical examples are presented to validate the robustness and accuracy of our numerical schemes.(c) 2021 Elsevier Inc. All rights reserved.