WENO Schemes for Balance Laws with Spatially Varying Flux

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Abstract

In this paper we are concerned with the construction of numerical schemes of high order of accuracy for hyperbolic balance law systems with spatially variable flux function, as well as with a source term of geometrical type. We start with the original finite difference componentwise weighted essentially nonoscillatory (WENO) schemes and then we create new schemes by modifying the flux formulations (locally Lax-Friedrichs and Roe with entropy fix) since flux is spatially variable, and by decomposing the source term in order to obtain balance between numerical approximations of the flux gradient and of the source term. We apply so extended WENO schemes to one-dimensional open channel flow equations and one-dimensional elastic wave equations. In particular, we prove that in these applications the new schemes are exactly consistent with appropriately chosen subset of steady state solutions. Experimentally obtaine

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