A new general method to compute dispersion errors on Cartesian stretched meshes for both linear and non-linear operators

Abstract

The present article presents a new analysis for the dispersion error and the methodology to evaluate it numerically. Here we present the spectral properties of several convective schemes, including non-linear ones, on Cartesian stretched grids for linear advection problems. Results obtained with this method when applied to uniform structured meshes, converge to the results obtained with the classical method for all the studied schemes. Additionally, effects on the time step depending on which scheme is used are considered using the proposed method. The extracted conclusions taken into account both errors and computational cost allow to propose an optimal scheme according to the selected meshing strategy.