相场移动接触线模型的数值近似：含变密度和粘度
Numerical Approximations for a Phase-Field Moving Contact Line Model with Variable Densities and Viscosities
AI总结：
本文提出两种高效能量稳定的数值方案，用于求解包含可变密度和粘度的两相流体耦合相场模型，验证了方案的准确性和效率。
摘要：
我们考虑了包含可变密度、粘度和移动接触线边界条件的两相流体耦合相场模型的数值近似。该模型是一个非线性耦合系统，由不可压缩纳维-斯托克斯方程和广义纳维边界条件以及具有移动接触线边界条件的卡恩-希尔利德方程组成。通过一些巧妙的显式-隐式处理非线性项，我们开发了两种高效、无条件能量稳定的数值方案，特别是针对静态接触线条件的线性解耦能量稳定方案，以及针对动态接触线条件的非线性能量稳定方案。为了验证所提方案的精度和效率，实施了高效的谱-伽辽金空间离散化。各种数值结果表明，所提出的方案是高效且准确的。
英文摘要：
We consider the numerical approximations of a two-phase hydrodynamics coupled phase-field model that incorporates the variable densities, viscosities and moving contact line boundary conditions. The model is a nonlinear, coupled system that consists of incompressible Navier--Stokes equations with the generalized Navier boundary condition, and the Cahn--Hilliard equations with moving contact line boundary conditions. By some subtle explicit--implicit treatments to nonlinear terms, we develop two efficient, unconditionally energy stable numerical schemes, in particular, a linear decoupled energy stable scheme for the system with static contact line condition, and a nonlinear energy stable scheme for the system with dynamic contact line condition. An efficient spectral-Galerkin spatial discretization is implemented to verify the accuracy and efficiency of proposed schemes. Various numerical results show that the proposed schemes are efficient and accurate.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
