We address the issue of point value reconstructions from cell averages in the context of third order finite volume schemes . In fact, most techniques known inthe literature rely on the creation of ghost cells outside the boundary and on extrapolation from the inside that, taking into account theboundary conditions, fills the ghost cells with appropriate values . In this paper, extending that approach, which does not make use of ghostcells, we propose a more accurate reconstruction for the one-dimensional case and a two-dimensional one for Cartesian grids . In several numerical tests wecompare the novel reconstruction with the standard approach using ghost cells, in fact, to a novel reconstruction using a different stencil, biased towards the interior of the domain . We propose a new reconstruction of the one and the two- dimensional case for the two and three-dimensional cases .

Author(s) : M. Semplice, E. Travaglia, G. Puppo

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Keywords : dimensional - reconstruction - cells - ghost - propose -

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