2021/03/23 by Matteo Semplice, M. Semplice, E. Travaglia +5 · 2 citations
Computer Science · Engineering · Mathematics · #65M08 76M12 #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Numerical Analysis (math.NA) #cs.NA #math.NA #msc:65M08 #msc:76M12
paper · pdf · doi:10.48550/arxiv.2103.12386
arxiv created 2021/03/23 · openalex publication_date 2021/03/23 · arxiv updated 2021/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We address the issue of point value reconstructions from cell averages in the context of third order finite volume schemes, focusing in particular on the cells close to the boundaries of the domain. In fact, most techniques known in the literature rely on the creation of ghost cells outside the boundary and on some form of extrapolation from the inside that, taking into account the boundary conditions, fills the ghost cells with appropriate values, so that a standard reconstruction can be applied also in boundary cells. In (Naumann, Kolb, Semplice, 2018), motivated by the difficulty of choosing appropriate boundary conditions at the internal nodes of a network, a different technique was explored that avoids the use of ghost cells, but instead employs for the boundary cells a different stencil, biased towards the interior of the domain. In this paper, extending that approach, which does not make use of ghost cells, we propose a more accurate reconstruction for the one-dimensional case and a two-dimensional one for Cartesian grids. In several numerical tests we compare the novel reconstruction with the standard approach using ghost cells.