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 L<sup>2</sup>(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.
Muscl reconstruction and haar wavelets
Gosse L
2015
Abstract
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.File in questo prodotto:
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