Mixed incompressible Navier-Stokes

43

I do not have time to look at this at the moment. i would suggest solving a stokes problem to get a Good initial flow profile for the problem.

44

A question for the non-dimensional form: in the book, the Re number appears only in front of the advection term. How is that? When I non-dimensioalise, I have the Re in front of the whole material derivative (=time derivative and advective term).

45

I would read section 4.2 of Scaling of Differential equations by Langtangen and Pedersen which present multiple variations for scaling the Navier Stokes equation

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46

Sometimes, only the pressure boundary conditions are given rather than \mathbf{g}_N ​. The correct boundary conditon should be p\mathbf{n}-\nu \frac{\partial\mathbf{u}}{\partial\mathbf{n}}=\mathbf{g}_N ，but it won’t converge. When I modified the boundary conditions as p\mathbf{n}= \mathbf{g}_N , it converges.

Here are the differences of the FEniCS code:

(dot(pressure_inflow*n, v) - dot(nu*nabla_grad(u)*n, v))*ds(marker_inflow)

(dot(pressure_inflow*n, v))*ds(marker_inflow)

Which are correct?