AN ANISOTROPIC ARTIFICIAL VISCOSITY METHOD - APPLICATION TO THE SIMULATION OF COMPRESSIBLE VISCOUS FLOWS

In this paper, we present a new artificial diffusion method to be used with a centered discretization of a set of convection dominated equat ions. The basic idea of the method is to add to each of these equation s a nonlinear diffusion term related to the regularity of the solution . The diffusion term is a function of the tendency of the scheme to ge nerate ripples; it is anisotropic, it depends on mesh orientation, and it is such that no artificial diffusion is added in areas where the s olution is free of oscillations. In order to show the capabilities of this method, we apply it to the resolution of the compressible Navier- Stokes equations using a finite element approximation. Results of nume rical experiments at transonic and supersonic regimes with moderate Re ynolds numbers are presented. Although we present only results for the Navier-Stokes equations, our artificial viscosity method is general i n the sense that it can be used with most sets of convection dominated equations, in one, two or three-space dimensions.