Séminaire
We present a novel dynamically adaptive numerical method for solving partial differential equations on the sphere. The method is based on second generation spherical wavelets on almost uniform nested spherical triangular grids, and is an extension of the adaptive wavelet collocation method to curved manifolds. Wavelet decomposition is used for grid adaption and restriction/prolongation on the adapted grid. An O(N) hierarchical finite difference scheme based on the wavelet multilevel decomposition is used to approximate the Laplace-Beltrami, Jacobian and flux-divergence operators using a conservative finite volume approximation based on hexagonal Voronoi cells. The accuracy and efficiency of the method is demonstrated using linear and nonlinear examples relevant to geophysical flows. This numerically scheme has been designed to provide a dynamically adaptive core for the solution of geophysical flows (e.g. shallow water equation) on the sphere.
Riwal Plougonven,
LMD-ENS, 24 rue Lhomond, 75 005 Paris
tel: 01 44 32 27 31, mel: plougon@lmd.ens.fr