Influence of the Artificial Dissipation Model on the Propagation of Acoustic and Entropy Waves

Abstract

The aim of this work is to show that the form of the artificial dissipation terms used in central-difference-type schemes to stabilise the solution of the unsteady Euler equations may play a crucial role on the propagation of entropy, vorticity and acoustic waves. It will be demonstrated by means of numerical experiments and theoretical analysis that the scalar formulation of the artificial viscosity prevents the correct propagation of entropy and vorticity waves for moderate low Mach numbers and that the upstream propagation of acoustic waves degrades significantly for high subsonic flows. It will be proved that if the scaling of the dissipative terms takes into account the fact that the entropy and acoustic waves may propagate at quite different velocities, the accuracy of the scheme is greatly improved. Actually it will be demonstrated that there exists a class of problems for which the standard scheme is unable to produce equivalent solutions to the ones obtained by the matricial model, without a large penalty in the number of points.