понедельник, 1 июня 2020 г., 6:14:49 UTC+3 пользователь Wolfgang Bangerth
написал:
>
> On 5/29/20 9:42 AM, Alexey Ozeritskiy wrote:
> >
> > In step-35 we find u^{k+1} (diffusion step)
> > Then we find \phi^{k+1} (projection step) and correct p^{k+1} pressure.
> > But why we don't correct u^{k+1} velocity? I think u^{k+1} must be
> solenoidal
> > but it is not.
>
> Alexey,
> I'm not enough of an expert on projection methods, but you might want to
> try
> the review paper by Guermond from a few years ago to get some of the
> background of these methods. I don't know whether u^{k+1} must be
> solenoidal,
> but it is quite possible that it doesn't have to be -- only that the
> divergence is small (some power of h).
>
Thanks, the answer is in the papers (Guermond, 1995, eq 5.11, Guermond,
1998, eq 3.5). Actually we find and use non-solenoidal (intermediate) u^k
on the diffusion step.
"The _projected_ velocity can be completely _eliminated_ from the algorithm
and the _intermediate_ velocity is the only one of interest." (Guermond,
1998)
As I understand, we don't need the projected (solenoidal) velocity for the
calculation.
>
> Best
> W.
>
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: [email protected]
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> www: http://www.math.colostate.edu/~bangerth/
>
>
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