Abstract
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.
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