[insta]

Hello
Ive a question about the non-linear term (convection term) in N.S equations : (u*nabla)u
I want to modify this term into : ((u+u0)*nabla)(u+u0)
I mean u=u+u0
where u0 is defind as some known function ,
can someone please give me a direction on how to do this?

ThankYou

[Bernhard]

Did you derive what the discretized equation should look like? Maybe you can treat all the terms that are not u*nabla u as a source?

By the way, what is the physics in this approach? It seems a bit weird here? Maybe you want to use u0 as initialization?

[insta]

This form of equation represent the nonlinear dynamics of the perturbations only and u0 is the basic flow, so u is vector of perturbations and p is the fluctuated pressure only. in the convective term
((u+u0)*nabla)(u+u0): (u0*nabla)u0 is identically zero and the basic pressure plus the laplace term for u0 constitute the basic velocity u0, so also these terms falls , and then you get the dynamics of the perturbations

Thanks for the advice I will try to understand your suggestion

[insta]

Hi bernard
About your suggestion

Maybe you can treat all the terms that are not u*nabla u as a source

I believe that is not possible because there are terms like '(u0*nabla)u' and
'(u*nabla)u0' ,and these terms cannot be treated as source terms, because they are depended on 'u'.
Thus they have to be treated as implicit terms like (u*nabla)u.
So, how do we implement these modifications?
Should we modify the matrix only or also the PISO loop?

Thanks

[levka]

Hey, guys have a look there
PISO algorithm for particular NS equation (special convection term)

Regards
Lev