# Expected computational time for DNS computation of fluid flow

Using an established criterion involving capturing eddies down to the Kolmogorov length scale it can be reasoned that the order of grid points in the computational mesh needs to be $N^3 \ge Re^{9/4}$ where Re is the Reynolds number of the flow. If $Re \approx 50,000$ then I get about $N^3 \approx 3.7\times 10^{10}$. I know very little about CFD but I am wondering if this is a outrageous requirement given today's high performance computers?

I can get access to nodes of a supercomputer cluster. Im not sure of the exact specifications of the cluster, nor which specs are relevant for our purposes of calculating the total time, so if someone could make an assumption and base their calculations on this spec, I could modify my expected computing time once I know what im dealing with.

• What specifically do you want to simulate? Nov 29 '14 at 21:38
• Thanks for your response- I want to simulate flow over an airfoil or if possible a full 3D compressor blade in an annulus. Dec 1 '14 at 21:36
• As Bill commented, generally this would be done using RANS or LES on account of the expense inherent in tackling such a geometry. Nothing says you can't directly simulate it aside from the cost, however, so if you can get the allocation and believe you can provide good inflow and outflow treatment, Godspeed. Dec 2 '14 at 2:24

$3.7\cdot 10^{10}$ is feasible today on the very largest of computers, but barely so. Recall that you also have to do a lot of time steps (with shorter time step size the larger the Reynolds number is), so it is important that the local problems on every processor remain small. A reasonable number of unknowns per processor may be 100,000 which would translate to needing 370,000 processors -- possible today, but definitely not easily.
We have people doing $4096^3$ and $8192^3$ mesh points 3D domains on our systems at TACC using 16384 cores (1024 nodes). These simulations take months of running time to achieve the results the scientists want.
Your Reynolds number is equivalent to a $\sim 3332^3$ domain, which is smaller than what we have running on our systems, but not by much. You're going to need a large computer, but not, by a fair amount, the largest in the world.