两相流运动接触线的能量稳定有限元法
An Energy-stable Finite Element Method for the Simulation of Moving Contact Lines in Two-phase Flows
摘要：
我们考虑两相流体的动力学，特别是移动的接触线，在固体基板上。动态由锐界面模型组成的不可压缩的Navier-Stokes \slash Stokes方程与经典的界面条件，Navier边界条件的滑移速度沿壁和接触线条件，其中涉及的动态接触角的界面接触线速度。我们提出了一个有效的数值方法的模型。该方法结合了有限元方法的Navier-Stokes/Stokes方程的运动网格与参数有限元方法的流体界面的动力学。接触线条件被制定为一个依赖于时间的罗宾型边界条件的接口，所以它是自然施加在弱形式的接触线模型。对于纳维-斯托克斯方程，数值格式遵循与连续介质模型相似的能量定律，但由于数值解在移动网格上的插值而产生误差。与此相反，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。数值算例验证了数值方法的收敛性和精度。
英文摘要：
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.
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。
