Dear friends,

I am trying to implement FAS to our current SIMPLE 3D code which is based on a staggered uniform grid. Our problem is a buoyancy convection problem. And a special point is that the density is a function of temperature and concentration.

Now I am not so sure on how to design the restriction scheme to guarrantee the mass balance. I know this is not hard when density rho is assumed a constant. But when it is a function of temperature and concentration, the situation changed.

For example, when we have the accurate solution on the finest solution. We have the relationship (rho_west*u)+(rho_east*u)+(rho_north*v)+(rho_south *v)=0

But when we restrict u and v to a coarser grid, this relation is not true any more because the density need be recalculated by the restricted temperature distribution, and especially for a staggered grid, the density at a face is the average of density at two center point.

Can I just neglect the above error and restrict u,v,T as what people have done in the constant density cases?

Thank you.

Since you consider a staggered grid, if you conservatively restrict temperature and concentration, your computed density will be automatically made conservative as well.

Well, that's definitely true if you consider *agglomeration* to generate the coarser cells. That implies that all finer cells are wholly contained within the coarse cell.

Do you average by the cell volume to restrict properties? Such as:

q_coarse = (1/V_coarse) SUM_{i=1}^{number of volumes within coarse mesh} V_i q_i

where i are the cells of the finer mesh contained within the coarse cell.