AN ARTIFICIAL DISSIPATION SCHEME FOR THE NAVIER‐STOKES EQUATIONS

Abstract

Isotropic artificial dissipation is added to the Navier‐Stokes equations along with a correction term which cancels the artificial dissipation term in the limit when the mesh size is zero. For a finite mesh size, the correction term replaces the artificial viscosity terms with hyperviscosity terms, i.e., with an artificial dissipation which depends on the fourth derivatives of the velocity. Hyperviscosity more effectively suppresses the higher wave number modes and has a smaller effect on the inertial modes of the flow field than does artificial viscosity. This scheme is implemented using the finite element method and therefore the required amount of dissipation is determined by analysing the discretization on a finite element. The scheme is used to simulate the flow in a driven cavity and over a backward facing step and the results are compared to existing results for these cases.