Precise modeling of contact angle is ubiquitous in capillary driven multiphase flow simulations. From a simple 2D rectangular capillary benchmark, we demonstrate and discuss the dependence of capillary dynamics on the mesh size with respect to Washburn’s equation. Mesh-dependency is dominated by an underestimation of viscous losses for coarser meshes and transits to ever increasing stress-related errors due the Navier–Stokes equations breaking down in the vicinity of moving contact lines subjected to several known boundary conditions. Furthermore, computational limits generally impose mesh sizes for which none of the errors are negligible. We show that for Washburn-like flows, a simple modification of the static contact angle value is adequate to correct the dynamics of the flow. This semi-analytic correction has the advantage of requiring no modification of the source code or implementation of new boundary conditions, and thus can be easily used with any codes whether commercial or not. Simulations of a self-coalescence module and a capillary pump are presented as 3D verification test cases of the method.

接触角的精确建模在毛细管驱动的多相流模拟中无处不在。从一个简单的 2D 矩形毛细管基准，我们展示并讨论了毛细管动力学对网格尺寸的依赖关系，关于沃什伯恩方程。由于纳维-斯托克斯方程在受几个已知边界条件影响的移动接触线附近失效，因此网格依赖性主要是对较粗网格的粘性损失的低估和过渡到与应力相关的误差不断增加。此外，计算限制通常会施加任何误差都不可忽略的网格尺寸。我们表明，对于类似 Washburn 的流动，静态接触角值的简单修改足以纠正流动的动力学。这种半解析修正的优点是不需要修改源代码或实现新的边界条件，因此可以很容易地与任何商业或非商业代码一起使用。自聚结模块和毛细管泵的模拟被呈现为该方法的 3D 验证测试用例。