FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method, Part II: Advection operator and slope limiting

摘要

This is the second in a series of papers on implementing a discontinuous Galerkin (DG) method as an open source NIATLAB/GNU Octave toolbox. The intention of this ongoing project is to offer a rapid prototyping package for application development using DG methods. The implementation relies on fully vectorized matrix/vector operations and is comprehensively documented. Particular attention was paid to maintaining a direct mapping between discretization terms and code routines as well as to supporting the full code functionality in GNU Octave. The present work focuses on a two-dimensional time dependent linear advection equation with space/time-varying coefficients, and provides a general order implementation of several slope limiting schemes for the DG method. (C) 2016 Elsevier Ltd. All rights reserved.