Numerical solution of a rimming flow problem using a moving mesh method. (English) Zbl 1032.35021
Summary: We consider the evolution of a thin film of viscous fluid on the inside surface of a cylinder with the horizontal axis, rotating with a constant angular velocity about this axis. We use a lubrication approximation extended to the first order in the dimensionless film thickness (including the small effects of the variation of the film pressure across its thickness and the surface tension) and numerically we compute the time evolution of the film to a steady state.
MSC:
| 35A35 | Theoretical approximation in context of PDEs |
| 35L67 | Shocks and singularities for hyperbolic equations |
| 35L65 | Hyperbolic conservation laws |
| 76D08 | Lubrication theory |
| 76A20 | Thin fluid films |
| 41A60 | Asymptotic approximations, asymptotic expansions (steepest descent, etc.) |
| 65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
