Stability analysis of a Galerkin/Runge-Kutta Navier-Stokes discretisation on unstructured tetrahedral grids - Giles, M (1997)
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 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 algebraic and generalised stability, sufficient stability limits are obtained for both global and local timesteps for fully discrete algorithms using Runge-Kutta time integration. © 1997 Academic Press.