Smoothing length and cut-off length

sph_tudelft_nl · July 2020

From the new CaseTemplate.xml for 5.0 I see there is a new parameter _hdp

<coefh value="0.866025" comment="Coefficient to calculate the smoothing length (h=coefh*sqrt(3*dp^2) in 3D)" /> 
<_hdp value="2" comment="Coefficient to calculate the smoothing length (hdp=h/dp)" />

According to the comments the smoothing length is two things: hdp and h. In the Run.out there is another symbol H.

In Section 3.1 of the User's Guide https://github.com/DualSPHysics/DualSPHysics/wiki/3.-SPH-formulation

only kernels with an influence domain of 2 h are considered

Can you please clarify which is which? Is there any risk here that the notions of 'smoothing length' (length scale of kernel or suchlike) and 'cut-off length' (size of the influence domain or suchlike) are being confused? Hopefully these is some sense in making notation and commentaries consistent, in due course of course.

atish_d · July 2020

Hi @sph_tudelft_nl

From my experience, coefh and hdp are two methods for specifying the same parameter, the smoothing length 'h'. 'coefh' and 'hdp' are interchangeable , however one must note that when using 'coefh', h is calculated as h = coefhsqrt(3dp^2) (in 3D). If using 'hdp', h is calculated as h = hdp*dp, a rearrangement of the equation in the comment.

Hope this helps

sph_tudelft_nl · July 2020

@atish_d

I see your point, thanks. So does the underscore before hdp disable that xml element by silently ignoring it? I have also seen the # being used for the same purpose in the XML input file, indeed.

But probably what they mean with smoothing length is actually the cut-off length, the "true size" of the kernel, which is more directly relevant to design a working simulation. I also think that the terminology in the User's Guide does reflect a common usage (one I have been exposed to, at least).

I can propose a pull request once 5.0 is online, since this is in the open-source part of the bundle.

Alex · July 2020

Smoothing lenght is smoothing length! Wendland kernel is defined for 2h, so that 2 times the smoothing length.

In addition, hdp and coefh should be properly defined in the XML_GUIDE_v5

Regards

sph_tudelft_nl · July 2020

Any risk of confusion is cleared, thanks.

There are two ways one can set the smoothing length: one can disable either by tweaking its XML name. (I had missed the XML guide somehow, right!)
Perhaps to get it all right at first sight, one might also write more straightforwardly:

<coefh value="0.866025" comment="Coefficient to calculate the smoothing length (h=coefh*sqrt(3)*dp in 3D)" /> 
<_hdp value="2" comment="Coefficient to calculate the smoothing length (h=hdp*dp)" />

and by the way it stands out nicely thathdp = coefh*sqrt(3)in 3D.

h and H indicate the same smoothing length in the XML input and Run.out output (likewise for the pairs dp,Dx and coefh,CoefficientH);
And the kernel size (cut-off length) is 2h following doctrine. No discussion. One can then estimate how many particles are contained inside a kernel support at least in the initial lattice. Handy.

atish_d · July 2020

The cut-off length is characteristic of the kernel function used. I assume DualSPHysics uses kernels with a cut-off length of 2h due to computational efficiency. A good example is the Gaussian kernel, which takes a greater distance than 2h to reach near zero (it never really goes to zero), which makes the function inefficient.

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Smoothing length and cut-off length

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