# Water shock modeling with DualSPHysics

Hello everyone,

I'm trying to model the entry of a wedge into the water at constant speed with DualSPHysics and to determine the maximum effort of this shock. However, the effort I find with DualSPHysics is always much lower than the expected results (I use Wagner's analytical model).

My questions are therefore the following:

1) Is DualSPHysics well suited for water shock simulation?

2) What are the most important parameters to set for this type of problem?

I sincerely thank you for your help.

Good luck to all of you.

## Comments

The most important aspect is probably how you model viscosity. What model have you chosen and why?

Kind regards

I'm using "Laminar+SPS" with value 1e-06. It's seem more physical for me. But i'm not an SPH expert. What do you think ?

Also, I noticed that the smaller the inter-particle distance "dp" is, the more the effort decreases. Can someone explain me why?

I also find the SPS-LES formulation to be more physical than the artificial viscosity one. That is the primary reason I try to use it whenever it is stable enough for my simulations.

In regards to your inner-particle distance comment, remember you might not be looking at converged results yet. If you are seeking convergence of the effort, then do a few different simulations to see at which resolution does your simulation converge.

Have you tried googling for existing papers looking at shock modelling in SPH?

Kind regards

Thanks for your quick answers!

Yes I did a convergence study but the effort decreases too much. The final value is not physical.

I also searched the internet for articles but could not find anything convincing on the study of shock force.

Remember, if your numerical scheme converges to a result, be it physical or not, the numerics have shown the "truth" as they see it. This means that your numerical simulation is stable in the sense, that it produces the same result, even if you keep refining the discretization.

Therefore the next step is looking at the physics - perhaps the implementation of SPS-LES in DualSPHysics is mostly suited towards wave-breaking and less on explicit shock fronts which you are simulating. Perhaps "tuning" an artificial viscosity simulation to give you the right result in one known case and then use these parameters for other cases could prove more beneficial for you?

This would probably take a bit more of time to figure out, but it is very worthwhile in diving a bit deeper into it.

Usually there is always something slightly relevant on the internet - I advise skimming through and try googling using synonyms, sometimes terms are not used as they should be and the "treasure paper" is found under a synonym :-)

I hope you are able to figure something out!

Kind regards

Thank you very much for these tips! I will continue my research on this subject.

Yours sincerely

@HomerSPH

Please consider the approximations in Wagner's theory as well. If memory serves me well now without double checks, it has been thought for initial instants, only near the point of impact, for an incompressible flow, etc etc. Two reasons why the SPH impact is milder can be

Both tries will cost you compute time though.

Thank you @sph_tudelft_nl for taking the time to answer my question!

Indeed, Wagner's model has its limits. But I am still surprised to find such weak results with SPH. Regarding your remarks, they are very judicious and help me to understand some points. But :

1) I use Laminar+SPS for viscosity. It should therefore be related to physics. But it seems to me that in Wagner's model the effects of viscosity are neglected (if I am not talking nonsense).

2) I have tried to reduce the inter-particle distance but the effort only decreases when I refine.

By any chance, would you have an analytical model of shock effort as a function of time for a wedge? I look for this formula in the articles by Faltinsen or Zhao but I can't find anything that satisfies me.

@HomerSPH

1) I also think that viscosity is irrelevant for the bulk of the process, and Wagner did not consider it, for an impact is often too quick for viscous friction to develop. Your viscosity should rather aim to stabilise the SPH calculation as the need be.

2) Oops I overlooked that you mentioned it, sorry. Try to play with the compressibility, that is the speed of sound, that is

coefsoundin the xml file. In some tests of mine, this changed the depth reached by an object in a given time. So perhaps this relates to your problem of forces as well.3) Readings

Not sure if this is a perfect match. Give this a chance though: it is about spheres.

Tadd T. Truscott, Brenden P. Epps, and Alexandra H. Techet, ‘Unsteady Forces on Spheres during Free-Surface Water Entry’,

Journal of Fluid Mechanics704 (10 August 2012): 173–210, https://doi.org/10.1017/jfm.2012.232.We present a study of the forces during free-surface water entry of spheres of varying masses, diameters, and surface treatments. Previous studies have shown that the formation of a subsurface air cavity by a falling sphere is conditional upon impact speed and surface treatment. This study focuses on the forces experienced by the sphere in both cavity-forming and non-cavity-forming cases. Unsteady force estimates require accurate determination of the deceleration for both high and low mass ratios, especially as inertial and hydrodynamic effects approach equality. Using high-speed imaging, high-speed particle image velocimetry, and numerical simulation, we examine the nature of the forces in each case. The effect of mass ratio is shown, where a lighter sphere undergoes larger decelerations and more dramatic trajectory changes. In the non-cavity-forming cases, the forces are modulated by the growth and shedding of a strong, ring-like vortex structure. In the cavity-forming cases, little vorticity is shed by the sphere, and the forces are modulated by the unsteady pressure required for the opening and closing of the air cavity. A data-driven boundary-element-type method is developed to accurately describe the unsteady forces using cavity shape data from experiments.

Take into account that the dynamic boundary condition of DSPH is equivalent to a hydrophobic surface of the falling object. This relates to the distinction between the cavity/non-cavity forming cases.

For a study with SPH it is good to know that this exists

Pierre Maruzewski et al., ‘SPH High-Performance Computing Simulations of Rigid Solids Impacting the Free-Surface of Water’,

Journal of Hydraulic Research48, no. S1 (2010): 126–34, https://doi.org/10.1080/00221686.2010.9641253.Numerical simulations of water entries based on a three-dimensional parallelized Smoothed Particle Hydrodynamics (SPH) model developed by Ecole Centrale Nantes are presented. The aim of the paper is to show how such SPH simulations of complex 3D problems involving a free surface can be performed on a super computer like the IBM Blue Gene/L with 8,192 cores of Ecole polytechnique fédérale de Lausanne. The present paper thus presents the different techniques which had to be included into the SPH model to make possible such simulations. Memory handling, in particular, is a quite subtle issue because of constraints due to the use of a variable-h scheme. These improvements made possible the simulation of test cases involving hundreds of million particles computed by using thousands of cores. Speedup and efﬁciency of these parallel calculations are studied. The model capabilities are illustrated in the paper for two water entry problems, ﬁrstly, on a simple test case involving a sphere impacting the free surface at high velocity; and secondly, on a complex 3D geometry involving a ship hull impacting the free surface in forced motion. Sensitivity to spatial resolution is investigated as well in the case of the sphere water entry, and the ﬂow analysis is performed by comparing both experimental and theoretical reference results.

1) I agree with you!

2) I've never played with this setting before. It's a good track that I'm going to explore.

3) These are very good articles! Especially the second one which finally presents effort coefficients as a function of time. I will study them in detail. I am also interested in the problem of the sphere.

I sincerely thank you for your help! If new ideas come to your mind, do not hesitate to let me know.

The key issue is the speed of sound. You can play with coefsound as you were suggested or you can directly define the speed of sound of your problem. Other way around is to define the speed of system if you know maximum velocities during impacts

Regards

@HomerSPH

Reconnecting to the above, I understand you are busy with problems of water impact. If you want to explore the topic with experiments of plunging spheres you are good to go; I would be cautious with objects of arbitrary shapes. I found strange results with very plain cubes (see this issue https://github.com/DualSPHysics/DualSPHysics/issues/72) but not with spheres. So treble check before making strides.

Also, my suggestion would be to use the simplest Verlet algorithm for the time stepping (StepAlgorithm=2). It is mathematically sound, is fast and I have noted a few glitches with the other algorithm (issue https://github.com/DualSPHysics/DualSPHysics/issues/74)

For the rest, a last note is that with the 'dynamic boundary conditions' there is always a gap between fluid and object all over; whereas in real water impact problems this gap develops after a certain time and downstream of so-called 'contact lines'. Consider this when you evaluate results physically. This difference is an acknowledged feature of that modelling technique, not a mistake in itself. If you play around with the new 'modified dynamic boundary conditions' that remove this gap issue, I would be curious to read how it went.

@HomerSPH Correction. Verlet is StepAlgorithm=1. Sorry for the confusion.