# Why is this case unstable using SPS-LES?

Hello!

I am looking at the example folder for mDBC:

And running this case it works fine using artificial viscosity. If I then try to run the simulation using SPS-LES, with a kinematic viscosity of 1e-6, I get an unstable simulation, with a very weird force result generated by the simulation.

Could anyone explain to me how I could go about stabilizing this setup such that I can use SPS-LES?

Kind regards

## Comments

Hi Asalih3d,

Can you give us a bit more information about where and how it goes unstable?

Ben

There are people in this community far more skilled to answer this question, but I can give it a go. I previously asked a very similar question and it was answered by gfourtakas.

SPH is inherently afflicted by numerical errors. It can be shown theoretically, that the discrete interpolation error (how field variables are evaluated) scales with A_SPH = A(r,t) + O(h^2) + O(dp/h) (from the book "Fluid Mechanics and the SPH Method" Damien Violeau page 327/328). Which means the accuracy of SPH simulations does not converge with higher spatial resolution unlike other methods in CFD. Untreated, these errors emerge and accumulate, until field variables oscillate, or the integrity of the particle distribution cannot be maintained. Therefore, dissipative terms have to be used in order to stabilize the scheme and damp the emerging oscillations. Viscous forces dissipate energy, as well as the density diffusion (Delta SPH) formalism stabilizes. In your case, a kinematic viscosity as low as 10^-6 does not (most of the times) dissipate enough energy to stabilize the scheme. In the context of artificial viscosity, alpha = 0.01 is the adopted parameter among practitioners to perform inviscid simulations (see Meringolo et al. 2018) (which is weird, because one would expect alpha = 0, and this shows how much the damping effect is needed). The viscosity formulation "laminar+SPS" emerges from a more phenomenological ground, but may not be more useful than the artificial viscosity, since numerical stability is at risk unless a far greater (unphysical) amount of kinematic viscosity is employed.

I hope this helps and anyone who knows better is invited to teach me.

@Asalih3d Would it possible for you to share two representations of the same situation with the two viscosity models where you see the onset and build-up of a difference? I am seconding Ben here. I am thinking of a time history or flow field that you consider the most informing. It's only for the sake of "a picture saying more than a thousand words". Only if that's not too inconvenient please.

@Hannes I might be wrong while recalling this here, but Meringolo et al. do comment on some simulations with alpha=0 (purely inviscid momentum equation). An appropriate density-diffusion term in the mass conservation equation is sufficient to dissipate energy in pretty much the same amounts and development as a simulation with nonzero viscosity. Of course, the vorticity is not damped, so you see more whirls. They do not comment on 'noise'. Just thinking along. This is no objection to what you wrote above (thanks).

Hi everyone!

I will provide some more information about this issue some time next week. I want to provide some good force plots and explanation of my issues, that is why it will take a bit of time.

Sorry for the late answer.

Kind regards

Hi again everyone.

Sorry for the delay. I am not exactly sure what has happened, but when I reran the case I got results as expected, even when using SPS-LES. I must have made a mistake somewhere in my workflow.

Sorry for the false alarm.

Kind regards