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I am working with the equations for incompressible viscous fluid:

$$ \partial_t \vec{\omega} + (\vec{u}\cdot\nabla)\vec{\omega} = \nu\nabla^2\vec{\omega} $$ $$ \nabla^2 \vec{\psi} = -\vec{\omega} $$ $$ \vec{u}=\nabla \times \vec{\psi} $$

with an usual notation:

  • $\omega$ ... vorticity
  • $u$ ... velocity
  • $\nu$ ... kinematic viscosity
  • $\psi$ ... stream function

I need to discretize the system (by means of finite differences). Since this is very common tasks, the schemes must be somewhere available, but I was not lucky in googling this time. Could you please share a solution?

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    $\begingroup$ How come? If I type "vorticity equation finite difference" into google, I get 233,000 results. See here: google.com/… $\endgroup$ – Wolfgang Bangerth Jun 3 '16 at 3:59
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    $\begingroup$ One standard method is Chorin's method, also described on Wikipedia. It doesn't use the vorticity form, though. $\endgroup$ – David Ketcheson Jun 3 '16 at 10:58

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