[JoshuaB]

A question relating to understanding the Convective Courant Number (CCN):

I understand the number is determined locally as CCN=dt * vel / dx

I think the vel is considered normal to the face of interest. I imagine dx is taken as the cell in which the vel vector points into. Of course dt is globally set.

Now I understand that one would prefer to see the CCN<=1 as this means that that the amount of distance traveled in one time step is less than through the neighboring cell.

But what happens if the CCN>1? For example, let’s look at mass being transported. If say CCN =1.5 does that mean that half the mass ends up in the adjacent cell and half is placed two cells away (or however many required depending on the adjoining cell sizes)? That is, is the computational algorithm complex enough to take this into account? What happens if the adjacent cell is a wall? Then does the solver simply assume all the mass goes into that adjoining cell?

And if it does, then is the problems with the CCN being greater than 1 is that we lose some of the nearest cell interaction is loss as the mass from time step t to t+dt is skipping a cell? Hence the solution is not quite as accurate because some of this quantity (mass above) might have changed direction and gone into a different cell at time step t+2*dt had the CNN been <=1.

The reason I am so interested, is that I have a jet in my solution that has a fairly fast velocity but does not change much. However this region is fairly small so the capture it accurately I used a higher level of mesh in this area. I have other areas that are being affected by this fast moving flow but are moving slower and are really more of the regions of interest. Thus if I don’t sacrifice too much in accuracy I would like to increase the time step.

So I would first like to make sure I understand what is happening if the CCN goes above 1. Then I can better understand the risk I am taking.