[Moreza7]

Originally Posted by sbaffini

The diffusion term is the one that, when you heat up a solid in a point, will make that heat diffuse in the rest of the solid. That is, lower the local peak of the temperature and increase the temperature in the surrounding (or viceversa for a local freezing point). It works the same in fluids and, in its simplest form, it is a diffusivity times the Laplacian of some variable (temperature in my example).

Don't take me wrong but, maybe, you should step back from LES in order to first clarify some basic concepts. The major risk here is investing time without a proper return. Also, as LES involves both numerics, fluid dynamics and turbulence, a strong background in all of them is required in order to understand it.

Maybe you can still grasp some general concept, but then I see no point in trying to decode, say, the SGS kinetic energy equation. Just know that it is what it is and go over it.

Thank you very much.

I know the concept of convection, diffusion, and dissipation I just wanted to know how did you find out that part in the equation plays a diffusion role just by looking at the equation. Now it seems that you did it by your experience.

Best regards

[sbaffini]

Originally Posted by Moreza7

Thank you very much.

I know the concept of convection, diffusion, and dissipation I just wanted to know how did you find out that part in the equation plays a diffusion role just by looking at the equation. Now it seems that you did it by your experience.

Best regards

Yes, experience, but the same that you have then. If there is a PDE with a laplacian multiplied by a sort of molecular coefficient, then it always plays that role, no matter what (well, if given the correct sign, of course). The same goes for the convetive term.

Term XII in the equation of Sagaut is slightly more complex because it allows a spatially varying kinematic viscosity, so appears under the divergence, but it is still a diffusion term.

My experience is that you can understand better these things once you also start coding them. Then you will see that, no matter what, that term will always act in the same way. Let us assume that is constant and use an explicit, first order, Euler integration scheme with a second order central differentiation for the term XII, then the resulting equation you would be solving is (assuming also a 1D simpification):

q_i(n+1) = q_i(n) + dt * nu * (q_i+1(n)-2*q_i(n)+q_i-1(n))/dx^2+ dt * (other terms)

Now, all other terms equal, if q_i(n) is larger than the average of its neighbors, the discretization for our simplified term XII will return a negative value which, in turn, will lower the value of q_i at the next time step n+1, and increase it if it was lower than its neighbors average. It will always produce this effect, no matter which equation it is in.

It is just simple as this. Actually, this is pretty much all I know about diffusion

[FMDenaro]

Originally Posted by Moreza7

Thank you very much.

I know the concept of convection, diffusion, and dissipation I just wanted to know how did you find out that part in the equation plays a diffusion role just by looking at the equation. Now it seems that you did it by your experience.

Best regards

What you see in XII is a term like Div (d*Grad( )). This defines the diffusion of a specie...it could be a partial mass, the momentum, a form of energy depending on d and the variable.

[Moreza7]

Dear Paolo and Prof. Denaro,

Thank you very very much for your patience. It is a pleasure for me to see your replies.
I learned a lot from you in this forum.

I really appreciate it.

Kind regards