[Alucard]

Goodmorning,

I'm try to simulate the growth of a cristal using,as a basis, interfoam.
As i'm at the beginning, i consider as a first case, a simple 2D circle that grows at a constant velocity "Uoo". Alpha=1 in the circle and 0 outside.

So what i want to "see" it's just a simple circle that grows in time in my square domain.
If the basic alpha transport equation is something like that:

d(alpha)/dt+U*grad(alpha)=0

in my case I add a "second" velocity that is the envelope growth:

d(alpha)/dt+U*grad(alpha)+Ug*grad(alpha)=0

So if I initialise my U=0 (I 've not motion of my circle) and I impose a constant Ug, how it's possible to integrate correctly this term "Ug*grad(alpha)" in the equation?

I tried to replace directly U=Ug BUT the calculation of the phi fluxes is quite complicated and realted to Ueqn so I cannot do that easily.
I know perhaps is a dummy question but it's 10 days I'm trying to figure out how to solve it and I don't see a clever solution to that.


Thank you in advance.