Analysis of subdivision schemes for mean value Multiresolution on triangles

A. Cohen, S.M. Kaber, M. Postel
Laboratoire d'Analyse Numérique,
Université Pierre et Marie Curie
BC 187, 4 place Jussieu,
75252 Paris Cedex 05, FRANCE
e-mail: kaber,postel@ccr.jussieu.fr,cohen@ann.jussieu.fr

16 Septembre 1998

A multiresolution procedure is used to solve bidimensional hyperbolic conservation laws on triangular grids. Multiresolution for a polygonal domain is treated here by building a hierarchy of nested unstructured grids. At each time step the solution of the hyperbolic problem can be represented on a given level of resolution by its mean values on each triangle and also by the differences between these values and values computed by reconstruction from the coarser level. Different reconstruction schemes have been analyzed. The size of the differences is used as a criterium to choose the fluxes computation method: on the triangles where the differences are small the solution is smooth and the fluxes are computed by interpolation of the fluxes at the coarser level. Inversely, on triangles where the differences are larger than a tolerance level, fluxes are computed with a second order ENO scheme. A validation of the numerical order of accuracy as well as computing time comparisons are presented.