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Take the rotation of
to find

(8.55) 
with the vorticity
.
Vorticity is transported both by an advective process
(
) and by viscous diffusion.
Write the (divergencefree) velocity as the rotation of a
streaming function
:

(8.56) 
This does not determine
uniquely;
require that
.
Basic equations for the vorticity method:
Twodimensional case:
and
have only components:
Apply LaxWendroff to these equations:
Stability is again governed by the CFL condition

(8.63) 
In addition, the presence of diffusive terms implies the restriction

(8.64) 
Next: 8.2.2 Pressure Method
Up: 8.2 Incompressible Flow with
Previous: 8.2 Incompressible Flow with
Franz J. Vesely Oct 2005
See also: "Computational Physics  An Introduction," KluwerPlenum 2001