# MUSCL reconstruction and Haar wavelets

1 IAC - Istituto per le Applicazioni del Calcolo -Mauro Picone-

Abstract : MUSCL extensions {\it 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 $L^2\Re$. 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 $\frac 1 2$. However these high-order reconstructions aren-t likely to improve the handling of delicate nonlinear wave interactions in the involved case of systems of Conservation-Balance laws.

Keywords : Second-order resolution SOR MUSCL reconstruction Multi-resolution Analysis Haar wavelets Godunov scheme Well-balanced WB scheme slope-limiter Well-balanced WB scheme. wave interactions

Author: Laurent Gosse -

Source: https://hal.archives-ouvertes.fr/