An energy stable finite element scheme within arbitrary Lagrangian Eulerian (ALE) framework is derived for simulating the dynamics of millimetric droplets in contact with solid surfaces. Supporting surfaces considered may exhibit non--homogeneous properties which are incorporated into system through generalized Navier boundary conditions (GNBC). Numerical scheme is constructed such that the counterpart of (continuous) energy balance holds on the discrete level. This ensures that no spurious energy is introduced into the discrete system, i.e. the discrete formulation is stable in the energy norm. The newly proposed scheme is numerically validated to confirm the theoretical predictions. Of a particular interest is the case of droplet on a non-homogeneous inclined surface. This case shows the capabilities of the scheme to capture the complex droplet dynamics (sliding and rolling) while maintaining stability during the long time simulation.
翻译:在任意的Lagrangeian Eulelian(ALE)框架内,为模拟与固体表面接触的毫微克小滴的动态,产生了一个能源稳定元素计划。考虑的支撑面可能显示通过普遍导航边界条件(GNBC)纳入系统的非同源性特性。数值计划的构建使(连续)能源平衡的对应方维持在离散水平上。这确保了离散系统不引入虚假的能量,即离散配方在能源规范中是稳定的。新提议的计划经过数字验证,以确认理论预测。一个特别感兴趣的例子是非同源倾斜表面的滴子。这个案例显示了该计划在长期模拟期间捕捉复杂的滴动(滑动和滚动)的能力,同时保持稳定性。