Stokes problem description

[dgm2]

Hello could you add a brief description of the Stoke problem similar to the other tutorials? https://github.com/mathLab/PINA/blob/fefba810341379b51b9a49e59d45fd82d668b1bb/examples/problems/stokes.py referred to the run_stokes file

Best regards

[dario-coscia]

Hi @dgm2 ! Unfortunately on examples we do not put the mathematical formulations as you noticed. The problem formulation is the following:

$$ \begin{cases} -\Delta \mathbf{u}(x,y) + \nabla p(x,y) = 0\quad (x,y)\in\Omega \quad \texttt{momentum} \ \nabla\cdot\mathbf{u}(x,y)= 0\quad (x,y)\in\Omega \quad \texttt{continuity} \ ux(x,y) - 2(1-y^2) = 0 \quad (x,y)\in\Gamma{in} \quad \texttt{inlet}\ p(x,y) = 0 \quad (x,y)\in\Gamma{out} \quad \texttt{outlet}\ u(x,y) = 0 \quad (x,y)\in\Gamma{top}\cup\Gamma_{bot} \quad \texttt{wall}\ \end{cases} $$

Where $u(x,y)=[u_x(x,y), uy(x,y)]$ is a vectorial function, and $p$ is a scalar function. The domain is a square domain $\Omega = [-2,2]\times[-1,1]$, with $\Gamma{in}={-2}\times[-1,1]$, $\Gamma{out}={2}\times[-1,1]$, $\Gamma{top}=[-2,2] \times 1$, $\Gamma_{bot}=[-2,2] \times -1$.

I hope this will help😄