[Gfs-users] time-step dependency of the residual divergence tolerance: could it lead to large accumulation of many small errors ?

[Bernhard Braun]

Hi all,

I've been following this thread about the time-step dependency of the
residual divergence tolerance in gerris:

https://sourceforge.net/p/gfs/mailman/message/28145902/

> therefore it is better to set the residual to max(dt*divU) so that the
> effective volume change is Res_tol*h^2. Could you please confirm this ?
...
> Actually I wanted to understand why the initial residuals of each time
> step were scaled by the time step. Because with small time steps, the
> initial residual is already under the tolerance. But in any case, at
> least one iteration of the Poisson solver is performed and in practice
> it is sufficient to enforce incompressibility. However I don't know if
> there exist a case where this can be a problem.

Now I wonder if the increase in error tolerance for small time steps
could lead to some kind of accumulation effect, that eventually leads to
a large accumultated error
as a result of many small errors over many small time steps. Or in other
words: shouldn't the residual tolerance be scaled with the length of the
*total simulation* instead of a single time step ?


Or am I missing something ? (I lack the mathematical backround knowledge
about CFD error analysis to thouruoghly judge this from a theoretical
point of view ;-)

Thanks a lot in advance for any answers !

Bernhard

















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