Stability Analysis of a Galerkin/Runge–Kutta Navier–Stokes Discretisation on Unstructured Tetrahedral Grids
✍ Scribed by M.B. Giles
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 407 KB
- Volume
- 132
- Category
- Article
- ISSN
- 0021-9991
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✦ Synopsis
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. ᮊ 1997 Aca- demic Press