Stability analysis of Galerkin/Runge{Kutta Navier{Stokes discretisations on unstructured grids

This paper presents a timestep stability analysis for a class of discretisations applied to the linearised form of the Navier-Stokes equations on a 3D domain with periodic boundary conditions. Using a suitable deni-tion of the `perturbation energy ' it is shown that the energy is monotonically decreasing for both the origi-nal p.d.e. and the semi-discrete system of o.d.e.'s arising from a Galerkin discretisation on a tetrahedral grid. Us-ing recent theoretical results concerning algebraic and generalised stability, sucient stability limits are ob-tained for both global and local timesteps for fully dis-crete algorithms using Runge-Kutta time integration.