# Diffusive terms formulation in DualSPHysics

Dear developer,

Good afternoon.

In the diffusive terms treatment (momentum equation formulation), the default option is "1" with alpha = 0.01:

<parameter key="ViscoTreatment" value="1" comment="Viscosity formulation 1:Artificial, 2:Laminar+SPS (default=1)" />

<parameter key="Visco" value="0.01" comment="Viscosity value" /> % Note alpha can depend on the resolution. A value of 0.01 is recommended for near irrotational flows.

.......

The question is if the equation used in the default case is the Euler equation with the numerical correction (artificial viscosity):

......

There are cases simulated with laminar + SPS turbulence modelling in the examples, please? I.e. good results were achieved?

Thank you for your attention.

With best regards.

## Comments

Artificial viscosity is not a diffusive term treatment, that is sthg different such as deltaSPH

Artificial viscosity is a viscosity treatment.

Now, using new mDBC and new density diffusion terms (Fourtakas et al 2019) aims to be more stable so for some cases there is no need to use higher dissipation as the one obtained with artificial viscosity, so using laminar can be enough...

So it depends on the case applications and forces involved.

The rule should be always laminar, and if that is not stable enough, then you need to dissipate more using artificial viscosity that you can also control with the free parameter alpha.

Regards

Dear Alex,

Thanks for your response.

I am referring to te treatment of the diffusive terms in the momentum equation...

You can see some tests of SPH modellings in https://doi.org/10.1007/s40430-021-03158-3

I understand you when says that better modelling depends on the case.

...

So from what I understand the SPS turbulence modelling for small scales of turbulence did not lead to good results in DualSPHysics.

Thank you for your attention,

Best regards.

I think you have a misunderstanding in the last line. Alex is specifically saying that if you can get your case to run with laminar + SPS (in DualSPHysics the two are connected right now, i.e. when Alex says laminar he means laminar + SPS), then you should indeed use laminar+SPS. I would argue the exact same thing. Even if the turbulence model is not the best, having some modelling of turbulence is vital in CFD.

He is saying in some cases you have issues with dissipating enough energy in the numerical simulation - here artificial viscosity can be beneficial since you can control the dissipation with the free-parameter alpha. But please note that artificial viscosity is

nota turbulence model. It is only a way to increase or decrease dissipation in a numerical simulation, useful for high-shock simulations.KInd regards

Thanks, dear Asalih.

Best regards.