Applications and Novel Regularization of the Thin-Film Equation
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913518232535040 |
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| author | Pang, Khang Ee |
| author_facet | Pang, Khang Ee |
| contents | The classical no-slip boundary condition of the Navier-Stokes equations fails to describe the spreading motion of a droplet on a substrate due to the missing small-scale physics near the contact line. In this thesis, we introduce a novel regularization of the thin-film equation to model droplet spreading. The solution of the regularized thin-film equation -- the Geometric Thin-Film Equation is studied and characterized. Two robust numerical solvers are discussed, notably, a fast and mesh-free numerical scheme for simulating thin-film flows in two and three spatial dimensions. Moreover, we prove the regularity and convergence of the numerical solutions. The existence and uniqueness of the solution of the Geometric Thin-Film Equation with respect to a wide range of measure-valued initial conditions are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17187 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Applications and Novel Regularization of the Thin-Film Equation Pang, Khang Ee Fluid Dynamics Numerical Analysis 76A20 The classical no-slip boundary condition of the Navier-Stokes equations fails to describe the spreading motion of a droplet on a substrate due to the missing small-scale physics near the contact line. In this thesis, we introduce a novel regularization of the thin-film equation to model droplet spreading. The solution of the regularized thin-film equation -- the Geometric Thin-Film Equation is studied and characterized. Two robust numerical solvers are discussed, notably, a fast and mesh-free numerical scheme for simulating thin-film flows in two and three spatial dimensions. Moreover, we prove the regularity and convergence of the numerical solutions. The existence and uniqueness of the solution of the Geometric Thin-Film Equation with respect to a wide range of measure-valued initial conditions are also discussed. |
| title | Applications and Novel Regularization of the Thin-Film Equation |
| topic | Fluid Dynamics Numerical Analysis 76A20 |
| url | https://arxiv.org/abs/2409.17187 |