Information Content in Spectral Calculations

Abstract

It is well known that when one solves numerically, with the aid of higher order approximations, partial differential equations or systems one may get numerical oscillations. The oscillations may arise from different sources; e.g. incorrect treatment of the outflow boundaries in hyperbolic systems, mild non-linear instabilities, etc. One interesting class of numerical oscillations occurs when flows with extreme gradients, or local discontinuities, are simulated. The usual way of combating this manifestation of the Gibbs phenomenon is to introduce some kind of artificial viscosity (even TVD methods basically do this).