3. Solving the discretized Navier-Stokes equation by penalization and the augmented Lagrangian method
We begin by explaining the penalization method for the Stokes equation. To solve the Navier-Stokes equation, we use a semi-implicit time scheme where, at each time step, we solve a Stokes problem by taking the convective term's value at the previous instant. Thus, knowing u k , v k and p k we determine u k +1 , v k +1 and p k +1 by solving for k = 0, 1, ... the following problem:
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Solving the discretized Navier-Stokes equation by penalization and the augmented Lagrangian method
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