Simulation time vs. Simulation Cell Count
Hi Guys!
This may seen like a trivial question to be asking, but I am trying to find out what the relationship between the number of nodes in a simulation and the total simulation time. Assuming a steady flow simulation, where the physics is consistent between simulations, is the relationship between cell count and simulation time a linear or non linear relationship? If it is a non linear relationship, what kind of relationship should it be? X^2, exponential? Any information would be great! Regards, Chris 
Ideally, a solver should scale as N^3 for 3d calculations and N^2 for 2.... but most solvers don't because of implementation and communication issues!

Any ideas why a 3D mesh would appear to have a linear relationship between cell count and simulation time? Maybe the range of cell count is not large enough to show the N^3 relationship? Or are there likely to be underlying issues at work here that need investigated?

Are we talking about a single core run, or a parallel run?

Hi,
Thanks for the feedback by the way, I really appreciate it. I'm just a bit puzzled as to why I'm seeing this. It's a single core run. Mesh independence studies have been conducted and the final chosen mesh correlates well with experimental data, but when I plotted simulation time vs cell count from the independence studies the relationship came out near enough linear.The range of cell values is 1.5  2.5 million cells. Within the simulation there are three idential meshes overlaid, flow is passing between these three regions via a 1D model (UDF), could this perhaps be the cause of such a phenomenon? Thanks 
hm, maybe I misunderstood you.... if you are considering the TOTAL amount of mesh cells / DOFs / nodes, then you would indeed expect a linear behavior  at least in a certain range...
when i mentioned the n^3 or n^2 behavior, I was referering to N being the number of cells in ONE grid direction only. linear scale up with total N is perfectly fine! 
Yes, I am talking about totalcell count in the mesh. I'm glad someone agrees with me that the linear relationship is ok.
My thoughts on the matter were that the solution time per cell should remain fairly constant, so if the total mesh time increases, then the total solution time should increase relative to the increase in cell count. Thanks for your help. 
It is very much dependent on the type of solver you are using. Multigrid can scale linearly with the number of cells in the system. If you use one of the older techniques such as SOR then it will not (at least not for larger mesh sizes).

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