The pressure signal in simulations of weakly compressible SPH. The presentation

This deposit contains the slideshow supporting the presentation at the 19th SPHERIC World Conference held in Barcelona, Spain on 17-19 June 2025, with SPHERIC standing for the Smoothed Particle Hydrodynamics Research and Engineering International Community.

This slideshow presents the research progress with respect to the 3-page summary submitted for selection in January, published in the Book of Abstract and available with figures from a separate Zenodo deposit.

Document distribution

The DOI 10.5281/zenodo.15661272 always retrieves the latest version of this one record and is the most convenient pointer to this work. The presentation is immediately available for viewing, reading and downloading in the default preview below. The file is open-access under the license Creative Commons Attribution Non Commercial Share Alike 4.0 International. This work can and should be cited as conveniently reported in the Citation box at the right of this web page.

Document research content

The talk has confirmed that changes of modelling options in the governing equations are clearly reflected in the low-frequency band of the pressure amplitude spectra. The basis of the diagnostic power of pressure spectra rests on the fundamental assumption of weak and artificial compressibility.

The talk has presented advances that generalise the insights of the summary. For example, the pressure is no longer measured at the solid boundary but at arbitrary fixed locations inside the domain. The pressure signal is obtained by applying the equation of state to the density of the particles in transit within a smoothing-kernel radius of those locations, rather than by using the momentum equation to compute the force averaged over a sensing surface. This makes any considerations independent of the standalone issue of boundary conditions, of derived variables and of concerns about the kernel not being populated by enough particles.

Likewise, monitoring the properties of the particles crossing a kernel-support region frees us from the obligation of recording the smoothed values only, and paves the avenue of expressing significant changes with other metrics like the maximum value.

Document organisation and delivery

The presentation leads the audience from the early insights reported at SPHERIC 2022 to the newest ones gained since the summary submission at SPHERIC 2025.

The topics selected for inclusion unroll in the following order:

• Part I: connection to previous work and milestones
• Part II: results from SPHERIC 2022
• Part III: baseline simulations for SPHERIC 2025
• Part IV: simulations without density diffusion for SPHERIC 2025
• Part V: ongoing work and conclusions

although sections may not mark the transitions explicitly.

The slideshow logic served the movements of the talk, whereby I could dwell on specific images and texts and glide over others as the speech rolled on. I managed proactively the expectation that I was there to comment on each and every detail on display. I asked the session moderator to show me a sign at each third of my time slot to ensure that this presentational strategy could be delivered without strain.

Document design and composition

The slideshow has been designed to support a 12' talk and, as you can tell now, for distribution after the event. The master slides are a slight customisation of the template provided by the Local Organising Committee. The document consists of 51 slides of which 24 are full-screen pictures to be fair to the richness of detail present in the results.

Given the particle-based nature of SPH, the physical space of detailed images (the flow in the corner of the tank) has been rendered using a pixel in FHD format (logical resolution 1920x1080 pixels) to represent the initial interparticle spacing. In this way the image canvas provides some intuition of the particle number density: empty pixels indicate absence of particles while more particles can still occupy the same pixel area. 

The text is written in the form of phrases more often than sentences because most visuals take a large canvas area. Hyperlinks (not always highlighted in colour, alas) point to integrations present in previous work, among which the summary submitted to the conference. Hyperlinks allowed me to free space for the results gained in the intervening six months. Sparse text indicates either shortage of preparation time or some sufficiency in the images that could be commented upon in spoken word.

Oversights happen. The conference year in the file name should be 2025 instead of 2022. Hyperlinks do not always stand out with a separate font colour and can only be identified by hovering on them with the mouse pointer (this is often the case for links to the Summary). In the graphs the colour for the lines of baseline and variant results is not consistent. Reference lines in the log-log graphs indicate first and second-order decay slopes, and this is not mentioned. These oversights can be fixed with a future deposit version.

Deposit version

The DOI 10.5281/zenodo.15661272 always retrieves the latest version of this record.

In the table below, major version numbers indicate changes in the deposit content, for which Zenodo always issues a new DOI. I use minor version numbers to indicate substantive changes in the text you are reading just now, the deposit's Description. 

Acknowledgements

Compute power supporting this deposit has been provided by NCC Netherlands, the EuroCC Project implementation in the Netherlands funded by the European High-Performance Computing Joint Undertaking (Grant Agreement 101101903).

The conversations on location with Matteo Antuono, Giuseppe Bilotta, Andrea Colagrossi, Jose M. Dominguez Alonso, Domenico Davide Meringolo and Damien Violeau are gratefully acknowledged too. That is what conferences are for.

Roel Jansen of 4TU.ResearchData, the Netherlands, kindly provided the usage metrics of the collection of datasets High-resolution SPH simulations of a 2D dam-break flow against a vertical wall.