Gradient flow formulation and second order numerical method for motion by mean curvature and contact line dynamics on rough surface
| Autor: | Jian-Guo Liu, Yuan Gao |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
Mean curvature Applied Mathematics Numerical analysis Dynamics (mechanics) Mathematical analysis Fluid Dynamics (physics.flu-dyn) FOS: Physical sciences Numerical Analysis (math.NA) Physics - Fluid Dynamics System of linear equations 35R35 35K93 65M06 76T30 01 natural sciences 010305 fluids & plasmas Physics::Fluid Dynamics Nonlinear system 0103 physical sciences FOS: Mathematics Capillary surface Mathematics - Numerical Analysis Viscous stress tensor Balanced flow 010306 general physics |
| Zdroj: | Interfaces and Free Boundaries. 23:103-158 |
| ISSN: | 1463-9963 |
| Popis: | We study the dynamics of a droplet moving on an inclined rough surface in the absence of inertial and viscous stress effects. In this case, the dynamics of the droplet is a purely geometric motion in terms of the wetting domain and the capillary surface. Using a single graph representation, we interpret this geometric motion as a gradient flow on a Hilbert manifold. We propose unconditionally stable first/second order numerical schemes to simulate this geometric motion of the droplet, which is described using motion by mean curvature coupled with moving contact lines. The schemes are based on (i) explicit moving boundaries, which decouple the dynamic updates of the contact lines and the capillary surface, (ii) a semi-Lagrangian method on moving grids and (iii) a predictor-corrector method with a nonlinear elliptic solver upto second order accuracy. For the case of quasi-static dynamics with continuous spatial variable in the numerical schemes, we prove the stability and convergence of the first/second order numerical schemes. To demonstrate the accuracy and long-time validation of the proposed schemes, several challenging computational examples - including breathing droplets, droplets on inhomogeneous rough surfaces and quasi-static Kelvin pendant droplets - are constructed and compared with exact solutions to quasi-static dynamics obtained by desingularized differential-algebraic system of equations (DAEs). 8 figures, 48 pages |
| Databáze: | OpenAIRE |
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