The Mathematical Institute, University of Oxford, Eprints Archive

Stability Analysis of Galerkin/Runge-Kutta Navier-Stokes Discretisations on Unstructured Grids

Giles, M. B. (1995) Stability Analysis of Galerkin/Runge-Kutta Navier-Stokes Discretisations on Unstructured Grids. Technical Report. Unspecified. (Submitted)

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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.

Item Type:Technical Report (Technical Report)
Subjects:D - G > Fluid mechanics
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1342
Deposited By:Lotti Ekert
Deposited On:12 Jun 2011 09:51
Last Modified:12 Jun 2011 09:51

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