论文标题
一种能量稳定的有限元方法，用于模拟两相流中的移动接触线
An Energy-stable Finite Element Method for the Simulation of Moving Contact Lines in Two-phase Flows
论文作者
论文摘要
我们将两相流体的动力学，特别是移动接触线的动力学在固体基板上。动力学由尖锐的接口模型控制，该模型由不可压缩的Navier-Stokes \ Slash Stokes方程与经典界面条件，沿墙壁的滑动速度的Navier边界条件以及将界面的动态触点角度与接触线速度相关联。我们为模型提出了一种有效的数值方法。该方法结合了用于移动网格上Navier-Stokes/Stokes方程的有限元方法，并使用用于流体接口动力学的参数有限元方法。接触线条件被配制为界面边界条件的时间依赖性robin类型，因此自然地以接触线模型的弱形式施加。对于Navier-Stokes方程，数值方案遵守与连续模型中类似的能量定律，但由于移动网格上数值解决方案的插值而导致误差。相比之下，对于Stokes流，不需要插值，因此我们可以证明数值方法在能量方面的全局无条件稳定性。提出了数值示例，以证明数值方法的收敛性和准确性。
We consider the dynamics of two-phase fluids, in particular the moving contact line, on a solid substrate. The dynamics are governed by the sharp-interface model consisting of the incompressible Navier-Stokes\slash Stokes equations with the classical interface conditions, the Navier boundary condition for the slip velocity along the wall and a contact line condition which relates the dynamic contact angle of the interface to the contact line velocity. We propose an efficient numerical method for the model. The method combines a finite element method for the Navier-Stokes/Stokes equations on a moving mesh with a parametric finite element method for the dynamics of the fluid interface. The contact line condition is formulated as a time-dependent Robin-type of boundary condition for the interface so it is naturally imposed in the weak form of the contact line model. For the Navier-Stokes equations, the numerical scheme obeys a similar energy law as in the continuum model but up to an error due to the interpolation of numerical solutions on the moving mesh. In contrast, for Stokes flows, the interpolation is not needed so we can prove the global unconditional stability of the numerical method in terms of the energy. Numerical examples are presented to demonstrate the convergence and accuracy of the numerical methods.
