Sousa, E. and Sobey, Ian (2002) A new perspective on the stability of unsteady streamfunction vorticity calculations. Technical Report. Unspecified. (Submitted)

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Abstract
The stability of a numerical solution of the NavierStokes equations is usually approached by considering the stability of an advectiondiffusion equation for either a velocity component, or in the case of twodimensional flow, the vorticity. Stability restrictions for discretised advectiondiffusion equations are a very serious constraint, particularly when a mesh is refined, so an accurate understanding of the stability of a numerical procedure is often of equal or greater importance than concerns with accuracy. The streamfunction vorticity formulation provides two equations, one an advectiondiffusion equation for vorticity and the other a Poisson equation between the vorticity and the streamfunction. These two equations are usually not coupled in stability considerations, commonly only the stability of time marching of the advection diffusion equation is taken into account. In this work, we derive a global timeiteration matrix for the full system and show that this iteration matrix is far more complicated than that for just the advectiondiffusion equation. We show how for a model system, the complete equations have much tighter stability constraints than would be predicted from the advectiondiffusion equation alone.
Item Type:  Technical Report (Technical Report) 

Subjects:  H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1225 
Deposited By:  Lotti Ekert 
Deposited On:  19 May 2011 06:37 
Last Modified:  29 May 2015 18:55 
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