2024/09/25 by Pang, Khang Ee
#76A20 #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2409.17187
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.