An energy stable algorithm for a quasi-incompressible hydrodynamic phase-field model of viscous fluid mixtures with variable densities and viscosities

作者：Gong, Yuezheng; Zhao, Jia; Wang, Qi^*

来源：Computer Physics Communications, 2017, 219: 20-34.

DOI：10.1016/j.cpc.2017.05.002

• Quasi-incompressible model
• Multiphase fluid flows
• Phase field
• Energy stable schemes

A quasi-incompressible hydrodynamic phase field model for flows of fluid mixtures of two incompressible viscous fluids of distinct densities and viscosities is derived by using the generalized Onsager principle, which warrants the variational structure, the mass conservation and energy dissipation law. We recast the model in an equivalent form and discretize the equivalent system in space firstly to arrive at a time dependent ordinary differential and algebraic equation (DAE) system, which preserves the mass conservation and energy dissipation law at the semi-discrete level. Then, we develop a temporal discretization scheme for the DAE system, where the mass conservation and the energy dissipation law are once again preserved at the fully discretized level. We prove that the fully discretized algorithm is unconditionally energy stable. Several numerical examples, including drop dynamics of viscous fluid drops immersed in another viscous fluid matrix and mixing dynamics of binary polymeric solutions, are presented to show the convergence property as well as the accuracy and efficiency of the new scheme.

• 出版日期2017-10
• 单位南京航空航天大学; 南开大学; 北京计算科学研究中心