In the not too distant future I will be looking to simulate lubricant oil flows in a gear box, with rotating gears located in a bath of oil. I will be looking at the distributions at various angles of incline. Generically, a model may look something like this:

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Does anybody have experience with Smoothed Particle Hydrodynamics (SPH) CFD packages that can provide advice on its limitations? I am less interested in absolute values of density/velocity etc., primarily I need to see the distribution of the fluid.

I am new to this branch of CFD and all I can find is advertising guff from the people who make the software and are trying to sell it. As I understand it, pre-processing time will be considerably lower than LES CFD since SPH does not require a mesh, where as an LES simulation would require a complex mesh with multiple rotating frames. Since we aren't looking at discrete volumes with SPH, instead at particles, the convection term is done away with making computation easier.

The companies selling SPH seem to be targeting exactly my application, I'm guessing that's for a good reason...

  • $\begingroup$ I'm beginning to think that I should move this question into the physics board, since SPH was developed for Astronomy initially... $\endgroup$ – Petrichor Jan 24 '18 at 8:34

I don't use SPH for fluid dynamics personally, but I've seen some presentations where it has been used for high strain rate material behavior which shares some effects (and equations) with standard fluid dynamics. SPH is good for large deformations and material separation processes. The German wikipedia article has a list of advantages and disadvantages of SPH which seem quite reasonable to me. I've tried to translate them to English; please edit this answer if the translation is not good enough. Note that I cannot really comment on the individual items.


  • SPH is a Lagrangian method with mass always conserved
  • very robust code, i.e. finds results under most circumstances
  • comparatively simple implementation, including testing of kernels
  • when using Gaussian normal distribution as kernel, allows interpretation of theoretical results quite easily
  • in modern codes, the calculation effort grows with $N \, \log N$, with $N$ being the number of particles
  • SPH shows good global results for a small number of particles


  • often, the code is too robust; i.e. using incorrect models, physically meaningless results can be calculated
  • error estimation is often problematic and can only be performed in comparison with other methods
  • SPH is highly dispersive
  • For good results, large particle numbers are required. Therefore it is usually not less computationally expensive than other methods
  • dealing with discontinuities is not easy, since structures on scales smaller than the smoothing length will be smoothed
  • $\begingroup$ Thanks for your input, helpful stuff and your English is great. $\endgroup$ – Petrichor Jan 24 '18 at 8:57

SPH is one of two different particle methods. SPH has limitations as discussed above. You may also want to look at Moving Particle Semi-Implicit method (MPS). This method is better for incompressible fluids and is used in engines and gearboxes. There is a case study and some videos on the website: https://enginsoftusa.com/Particleworks-CFD-Software.html


Robin's statements are valid, I would only recommend to use open source libraries like DualSPHysics, which is a quite fast, robust and well-documented SPH solver for a wide range of applications. Being open-source, it helps you to implement and configure your own or other's theories concerning the boundary conditions for moving gears. Although I never tried any of them, I don't believe that there are major benefits of using commercial SPH software today.


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