Spurious Behaviour of Numerically Computed Fluid Flow |
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Authors: | EASTWOOD, JAMES W. ARTER, WAYNE |
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Affiliation: | Culham Laboratory, Abingdon Oxfordshire, OX14 3DB, UK (Euratom/UKAEA Fusion Association) |
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Abstract: | We investigate the stability to aliasing errors of numericalschemes for hydrodynamics, taking the viscous Burgers' equationas a model for systems with a term that is quadratic in thevelocity. Considering wavelengths equal to three times the mesh-spacing,and arbitrary mean flow, we are able to demonstrate explicitlyfor common schemes (a) a sufficient criterion for stabilityand (b) blow-up of solutions in a finite time when (a) is violated.Singular behaviour is shown to persist at all wavelengths: studiesof wavelengths up to thirty times mesh-spacing make it clearthat a profile with a single region of strong convergent flowis most conducive to instability. In contrast, spectral (Galerkin)and upwind schemes are shown to be stable for all flows andperiods. |
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