Session Cd - Interfacial & Thin-Film Instabilities.
ORAL session, Sunday, November 23
304, Moscone Center
Lubrication equations are commonly used to describe thin films or liquid layers driven by surface tension. Recent studies of singularities, describing rupture of the fluid layer, show that such equations exhibit complex dynamics which can be difficult to simulate accurately. In particular, one must ensure that the numerical approximation of the interface does not show a false premature rupture. Generic finite difference schemes have the potential to manifest such instabilities especially when underresolved. We design a new numerical method that is guaranteed to have a positivity preserving property, regardless of the spatial resolution, whenever the PDE has such a property.