Modelagem e simulação do escoamento de películas finas em superfícies sólidas

Abstract

The present work aims at the study and implementation of numerical schemes for a class of problems modeled by high order partial differential equations, which are nonlinear. The problems considered arise in lubrication theory, where thin films made up of viscous fluids move in contact with solid surfaces. Such equations, in general of fourth order, can be degenerate. In fact, these models may have additional second-order singular terms, which commonly describe the effects of gravity and molecular interactions. Furthermore, a theoretical and numerical model is formulated to describe the dynamics of a thin layer of liquid on an inclined surface driven by gravity. This work uses the so-called spectral algorithm, which is a method for solving large nonlinear systems, which does not solve linear systems, nor does it use any explicit information associated with the Jacobian matrix. Numerical simulations characteristic of thin-film evolution are presented and the results obtained show that the spectral algorithm is an efficient method for the simulation of thin-film flows on solid surfaces.