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?