# Are additional particle stencils implemented with the density diffusion term of Fourtakas et al 2019

#### Topic

This is about the implementation of the density diffusion term in DualSPhysics 5.0. In the XML this is

<parameter key="DensityDT" value="1" comment="Density Diffusion Term 0:None, 1:Molteni, 2:Fourtakas, 3:Fourtakas(full) (default=0)" />

#### Reading

I have read the articles Fourtakas et al 2015 and Fourtakas et al 2019. (In passing, I do invite those tempted to look at them not to resist this temptation: personally I found both really pretty fine research expositions.)

In both articles the kernels of fluid particles approaching the boundary are endowed with *extra fictitious particles* *in the solid domain*. In this way there is no loss of information due to an half-full kernel. In both articles, the performance of this auxiliary stencil is improved by the inclusion of hydrostatic pressure/density in the particle properties.

In particular, in the latter article, the treatment is extended to 3D and to a delta-SPH mass conservation equation: there we get basically DensityDT=3, as far as I could understand from another post. So, DensityDT=3 is a density diffusion term extended to include the hydrostatic density. Fourtakas et al. 2019 makes it clear that this formulation does improve the performance of stencils (LUST is the acronym for them) near the solid boundaries.

So, according to the evidence brought forth in the article, *it is the pair stencil + extended deltaSPH that does the trick*.

#### Questions

I have not found mention of these stencils in the wiki at https://github.com/DualSPHysics/DualSPHysics/wiki/3.-SPH-formulation

- Are the (LUST) stencils of fictitious particles also implemented in DualSPHysics?
- If not, we only have the modified delta-SPH. Are the studies (articles, master theses, etc) on
*what happens when one implements DensityDT=3 without a special stencil*? Would you mind it to share those?

Thanks in advance for considering this.

## Comments

Hi,

In one of the tweets, they mentioned LUST as a boundary conditions they wish to implement in the future. From my understanding, there is no stencil particules. That's why they recommend using DensityDT=2, since it does no apply near boundaries.

I guess the full solution (=3 with LUST) is in the pipeline.

Kind regards

@TPouzol Thanks for the tips. I could not find a twitter re DualSPHysics and LUST in the wish list, although lust is quite a tricky search term :-) Anyhow an announcement of publication https://twitter.com/search?q=DualSPHysics%20LUST&src=typed_query is the nearest I could get to. I then got interested to know whether DensityDiffusion = 2 is the recommended version: would have a formal/informal source for this?

@sph_tudelft_nl

I cant find the reference to Lust anymore... and I bet it was not a sure thing, however in the wiki "10 DSPH futute", they say: "New boundary conditions."

Regarding densityDT =2 being the preferred option, I guess I concluded to that following the setup of many examples (dam break etc) where they use it. Also, this comment suggest it (https://forums.dual.sphysics.org/discussion/1783/why-use-fourtakas-full-in-ddt#latest):

"You have two options, either apply the diffusion term only to particles which do not interact with the fluid (that is 2

haway from the boundary, DDT2) or apply the term in the whole (full DDT3) domain. Clearly the latter will produce much more accurate pressure field near the boundary free from numerical noise . Nevertheless, a severely truncated kernel with high density boundary particles from DBC will impact the accuracy of this diffusive term."maybe I got it wrong...

The last update of DSPH is great by many aspects, even though some seems unfinished (like the mdbc that cannot work with imported geometry), it introduced many new aspects, but from a user point of view, things are more confusing right now IMO and seems like it is work in progress (not complaining, I do appreciate the work of the team! just sharing my thoughts).

@TPouzol mDBC can indeed work with imported geometry, you just have to play A LOT around with the settings, sometimes even increasing h to unreasonable numbers and also in the beta version of the release they had included a tool for normals calculation (which is not meant to be used), but I found a bit succes with. You can have a look at this thread:

https://forums.dual.sphysics.org/discussion/1788/normals-for-slightly-complex-surfaces-might-be-calculated-wrongly#latest

Here it worked on an imported stl.

@sph_tudelft_nl

I took a look at some of my old work and found this:

Which was in a chapter about future additions to DualSPHysics which I wrote about 2-3 years back. So indeed it was meant to be included at a time, but probably was put on back-burner due to mDBC and other interesting options.

Kind regards

Thanks to @TPouzol and @Asalih3d for thinking along and sharing your thoughts and findings. Appreciated. I put the original question back to the front solely to maintain focus on the original question. It is, of course, all very fine that stuff is in the making but, from the user's perspective, I would like to anticipate which effect the available options are intended for. Else, it is ill-used time to enable and test features that are rather meant to be stepping stones. The Developers will let us know what the state of the play is.

I have not found mention of these stencils in the wiki at https://github.com/DualSPHysics/DualSPHysics/wiki/3.-SPH-formulation

1. Are the (LUST) stencils of fictitious particles also implemented in DualSPHysics?

2. If not, we only have the modified delta-SPH. Are the studies (articles, master theses, etc) on ? Would you mind it to share those?

Thanks in advance for considering this.

Hi,

Let me clear up this if possible.

We have NOT released a the LUST BCs implementation nor the LUST stencils is implemented in the current version. I can not confirm that we will be releasing this BC.

The modified diffusion term is NOT LUST specific, it was developed as part of the work we did in LUST, but it is applicable to any BCs including DBCs and MDBCs as is the DDT_1 from Molteni and Colagrossi.

A recent publication is:

Fourtakas, G., Vacondio, R., Domínguez, J. M., & Rogers, B. D. (2020). Improved density diffusion term for long duration wave propagation. In

Proceedings of the International SPHERIC Workshop, Harbin, China.More to come! Thank you!

Regards,

George

Thanks @gfourtakas . All clear and quite helpful indeed. Back full circle to the top of the post, you are developing quite a good research tack: keep up the good work!

If I may ask a favour, would you mind sharing that conference contribution

Fourtakas, G., Vacondio, R., Domínguez, J. M., & Rogers, B. D. (2020). Improved density diffusion term for long duration wave propagation. In

Proceedings of the International SPHERIC Workshop, Harbin, China.with a link or attachment to the forum post? This could also remain for next forum visitors. At least now and for me, search machines did not help out, and the site to the Harbin workshop (http://spheric.hrbeu.edu.cn/) appears to be down or unresponsive.

Thanks in advance for considering this.

Proceedings from SPHERIC are not published online. Only private versions can be sent by authors to interested people.