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.