An adaptive moving mesh method for two-dimensional thin film flow equations with surface tension

In this paper, we extend our previous work (Alharbi and Naire, 2017) on a one-dimensional r-adaptive moving mesh technique based on a mesh density function and moving mesh partial differential equations (MMPDEs) to two dimensions. As a test problem, we consider the gravity-driven thin film flow down an inclined and pre-wetted plane including surface tension and a moving contact line. This technique accurately captures and resolves the moving contact line and associated fingering instability. Moreover, the computational effort is hugely reduced in comparison to a fixed uniform mesh. (C) 2019 Elsevier B.V. All rights reserved.