Kernel correction

amir

Hi
From reading this forum, I have found why the "Kernel Gradient Correction" is not implemented in the code.

But I have not found the reason for "Kernel Correction".

Can any one describe it to me?

Thanks

Alex

The kernel needs to be corrected when this is truncated:
- close to free-surface
- at interfaces
- close to boundaries
So kernel corrections means basically "normalisation" so Wab / sumWab

amir

Thank you Alex!
But I think this process is not carried out during the solution. Right?

Alex

note that Wab (kernel) is not used during DSPH execution, but derivative of Wab (in momentum and continuity equations)

kernel is only used in some post-processing tools such as MeasureTool in order to obtain values when sum_wab is more than a minimum value...
in this way we avoid to obtain magnitudes if the number of neighbours is too low for example and we normalise the kernel if sum_wab>0.5 (by default)

amir

Thanks for your fantastic reply!
In the post processing document, computing the velocity is:

V_a=sum (V_b*W_ab) / sum (W_ab)

So, this formulation is the "kernel correction". Right?

If the sum(W_ab) is less than 0.5, what would happen?

Alex

So, this formulation is the "kernel correction". Right?
YESSSS

If the sum(W_ab) is less than 0.5, what would happen?
Then a DUMMY value will be used.
Generally we use ZERO (for velocity for example)
or -9999999 (for pressure)

amir

So much thanks. In some references (e.g. Bonet & Lok (1999)) formula of the kernel correction is different. i.e. it contains mass and density.
See the attached picture.


Would you mind please explain it more?
Regards

Alex

that is more general in case MASS is variable, in the current code our mass is cte and density has small variations (so that volume has small variations), so the formula we used without the volume is accurate enough