velocity - when global or local

i’m beginner. I use CA method to get velocity in points in grid then i would like run LBM in each cell. To compute equilibrium distribution i use local velocity as result i get distribution function grid. How to consider speed of computed values in LBM?

I am sorry, but I do not understand what you are talking about. Could you clarify and provide more details?

in red points i have speed from other method. i would like use LBM but there is use local speed to compute the equilibrium distribution function. there are equations:

u_x(j,i) = u_x(j,i) + ex(k)*f(j,i,k)
u_y(j,i) = u_y(j,i) + ey(k)*f(j,i,k)

u_x(j,i) = u_x(j,i)/rho(j,i)
u_y(j,i) = u_y(j,i)/rho(j,i)

f(j,i,k) = f(j,i,k)-( f(j,i,k) - feq(j,i,k))/tau

i don’t know where use speed from red points

Dear Ola,

It depends which equation you want to restore. For the advection-diffusion equation you need only to calculate density locally and the velocity is externally provided. If you want to restore the Navier-Stokes equation you need to calculate velocity locally through the distribution populations.