Muscl reconstruction and haar wavelets

MUSCL extensions (Monotone Upstream-centered Schemes for Conservation Laws) of the Godunov numerical scheme for scalar conservation laws are shown to admit a rather simple reformulation when recast in the formalism of the Haar multi-resolution analysis of L²(R). By pursuing this wavelet reformulation, a seemingly new MUSCL-WB scheme is derived for advection-reaction equations which is stable for a Courant number up to 1 (instead of roughly 1/2 ). However these highorder reconstructions aren't likely to improve the handling of delicate nonlinear wave interactions in the involved case of systems of Conservation/Balance laws.