Median Filters for Anisotropic Wetting / Dewetting Problems
Copyright policy )Median Filters for Anisotropic Wetting / Dewetting Problems
We present new level set methods for multiphase, anisotropic (weighted) motion by mean curvature of networks, focusing on wetting-dewetting problems where one out of three phases is stationary -- a good testbed for checking whether complicated junction conditions are correctly enforced. The new schemes are vectorial median filters: The level set values at the next time step are determined by a sorting procedure performed on the most recent level set values. Detailed numerical convergence studies are presented, showing that the correct angle conditions at triple junctions (which include torque terms due to anisotropy) are indeed indirectly and automatically attained. Other standard benefits of level set methods, such as subgrid accuracy on uniform grids via interpolation and seamless treatment of topological changes, remain intact.
26 pages, 25 figures
- University of Michigan–Flint United States
Finite difference methods for boundary value problems involving PDEs, interfacial motion, Variational methods applied to problems in fluid mechanics, Flows related to mean curvature, Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), Quasilinear parabolic equations with mean curvature operator, Numerical Analysis (math.NA), PDEs in connection with fluid mechanics, 65M12, 35K93, threshold dynamics, wetting/dewetting, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, median filters, anisotropic surface tension, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Thin fluid films
Finite difference methods for boundary value problems involving PDEs, interfacial motion, Variational methods applied to problems in fluid mechanics, Flows related to mean curvature, Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), Quasilinear parabolic equations with mean curvature operator, Numerical Analysis (math.NA), PDEs in connection with fluid mechanics, 65M12, 35K93, threshold dynamics, wetting/dewetting, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, median filters, anisotropic surface tension, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Thin fluid films
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