Efficient implementation of WENO schemes to nonuniform meshes

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Abstract

Most of the standard papers about the WENO schemes consider their implementation to uniform meshes only. In that case the WENO reconstruction is preformed efficiently by using the algebraic expressions for evaluating the reconstruction values and the smoothness indicators from cell averages. The coefficients appearing in these expressions are constant, dependent just on the scheme order, not on the mesh size or the reconstruction function values, and can be found, for example, in Jiang, Shu, Efficient implementation of WENO schemes, J. Comp. Physics, 1996. In problems where the geometrical properties must be taken into account or the solution has localized fine scale structure that must be resolved, it is computationally efficient to do local grid refinement, and therefore also desirable to have numerical schemes, which can be applied to nonuniform meshes. Finite volume WENO schemes extend naturally to nonuni

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