Projection Method for Droplet Dynamics on Groove-Textured Surface with Merging and Splitting
نویسندگان
چکیده
The geometric motion of small droplets placed on an impermeable textured substrate is mainly driven by the capillary effect, competition among surface tensions three phases at moving contact lines, and obstacle. After introducing infinite dimensional manifold with admissible tangent space boundary manifold, Onsager's principle for obstacle problem, we derive associated parabolic variational inequalities. These inequalities can be used to simulate line dynamics unavoidable merging splitting due To efficiently solve inequality, propose unconditional stable explicit updating scheme coupled a projection method. decouples computation mean curvature lines. Meanwhile, step splits difficulties brought surface. Furthermore, prove stability present accuracy check. convergence proposed also proved using nonlinear Trotter-Kato's product formula under pinning assumption. incorporating phase transition information points, several challenging examples including are demonstrated.
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2022
ISSN: ['1095-7197', '1064-8275']
DOI: https://doi.org/10.1137/20m1338563