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An adaptive moving mesh method for two-dimensional thin film flow equations with surface tension. (English) Zbl 1444.76019
Summary: In this paper, we extend our previous work [the authors, ibid. 319, 365–384 (2017; Zbl 1457.76109)] 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.
MSC:
76A20 Thin fluid films
76M20 Finite difference methods applied to problems in fluid mechanics
76D45 Capillarity (surface tension) for incompressible viscous fluids
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
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