|Date:||Wed, September 7, 2011|
|Place:||Research I Seminar room|
Abstract: Particle methods are numerical methods for continuum dynamics in which the flow fields are discretized and transported along a finite discrete set of Lagrangian trajectories. Particle methods can be classified into those transporting vorticity and those transporting mass. We will consider the construction of a new potential vorticity method. The goal of this PhD-project is to develop a high order Lagrangian scheme for compressible flows, that overcomes a built-in problem of known Lagrangian schemes: high order schemes require the continuity equation to be solved as separate PDE. However, typical numerical schemes would lose the structure at the same time. We will try to use the advantage given by Ertel's potential vorticity theorem: it replaces the continuity equation by materially advected quantities which are trivial for a Lagrangian scheme.