A question on dealii tutorial step-35

[陈敏]

Dear all,

I have a question on the step-35 when I learn it.  the step use project method to solve NS equation. And for updating the pressure step, there is a Rotational Form.  In the function of update_pressure(const bool reinit_prec), it seem it plus the rotational term(+1/Re*div u), while the formula is minus(-1/Re*div u), the pres_tmp is calculated at projection_step, and is pres_tmp is (div u).

I want to know why here is plus not minus. Maybe the minus sign was included in the original code I didn't notice or understand.

Could anyone help me out?

Best,

Chen

[Wolfgang Bangerth]

Chen:

I'm not sure anyone still active in the project knows the program well, so I asked the author of the program, Abner Salgado, about the issue and this was his answer:

> What happens is that the pressure update equation, written right above
> the implementation of
>
> update_pressure
>
> is understood in "weak" form. We multiply by a test function in the
> pressure space and the divergence term is integrated by parts (hence the +).
>
> This is so because div u is not in the pressure space and so we cannot
> simply add the corresponding coefficient vectors.
>
> It involves solving a mass matrix problem, as it can be seen in the
> implementation.
>
> Hope this clarifies things.

I hope this helps!

Best

 Wolfgang

[hkch...@gmail.com]

Dear  Wolfgang Bangerth

Thank you and thank Abner Salgado. Now, I'm clear.

Best,

Chen