One- and Multi-dimensional CWENOZ Reconstructions for Implementing Boundary Conditions Without Ghost Cells

Abstract We address the issue of point value reconstructions from cell averages in context third-order finite volume schemes, focusing particular on cells close to boundaries domain. In fact, most techniques literature rely creation ghost outside boundary and some form extrapolation inside that, taking into account conditions, fills with appropriate values, so that a standard reconstruction can be applied also cells. Naumann et al. (Appl. Math. Comput. 325: 252–270. https://doi.org/10.1016/j.amc.2017.12.041 , 2018), motivated by difficulty choosing conditions at internal nodes network, different technique was explored avoids use cells, but instead employs for stencil, biased towards interior this paper, extending approach, which does not make we propose more accurate one-dimensional case two-dimensional one Cartesian grids. several numerical tests, compare novel approach using