Séminaire
Some finite difference techniques for the discretization of two- and three dimensional equations of motion of compressible and incompressible flows will be reviewed, which preserve discrete approximations of potential vorticity or potential enstrophy and extend on triangular/hexagonal meshes the potential enstropy preserving scheme proposed by Sadourny in 1975. Their accuracy will be compared to that of more standard discretization approaches, highlighting the increase in accuracy resulting from the use of these methods. The perspectives for further development and application of these methods in climate modelling and computational fluid dynamics will also be discussed.
References:
L. Bonaventura, T. Ringler, Analysis of Discrete Shallow-Water Models on Geodesic Delaunay Grids with C-Type Staggering, Monthly Weather Review, 133:2351-2373, 2005
A. Abba' and L. Bonaventura, A vorticity preserving finite difference discretization for the incompressible Navier-Stokes equations, International Journal of Numerical Methods in Fluids, 56:1101-1106, 2008
Riwal Plougonven
plougon @ lmd.ens.fr