Finite Volume Formulation of Compact Upwind and Central Schemes with Artificial Selective Damping

The present paper describes the use of compact upwind and compact central schemes in a Finite Volume formulation with an extension towards arbitrary meshes. The different schemes are analyzed and tested on several numerical experiments. A new formulation of artificial selective damping that is applicable on non-uniform Cartesian meshes is presented. Results are shown for a 1D advection equation, a 2D rotating Gaussian pulse and a subsonic inviscid vortical flow on uniform and non-uniform meshes and for a non-linear acoustic pulse.