STABILITY ANALYSIS OF A GALERKIN RUNGE-KUTTA NAVIER-STOKES DISCRETIZATION ON UNSTRUCTURED TETRAHEDRAL GRIDS/

This paper presents a timestep stability analysis for a class of discr etisations applied to the linearised form of the Navier-Stokes equatio ns on a 3D domain with periodic boundary conditions. Using a suitable definition of the ''perturbation energy'' it is shown that the energy is monotonically decreasing for both the original p.d.e. and the semi- discrete system of o.d.e.'s arising from a Galerkin discretisation on a tetrahedral grid. Using recent theoretical results concerning algebr aic and generalised stability, sufficient stability limits are obtaine d for both global and local timesteps for fully discrete algorithms us ing Runge-Kutta time integration. (C) 1997 Academic Press.