General questions on grid-based computing

Adrin Gharakhani

I have two general (and many sub- ) questions on grid-based computing. If you can answer any of them, especially on adaptivity, I would really appreciate it.

1) Automatic volumetric mesh generation:

What is the computational complexity of the state-of-the-art 3D mesh generators for Navier-Stokes? By complexity, of course, I mean what is the timing as a function of the number of nodes/cells/etc. If O(N) or O(NlogN) is the constant high?

Essentially, if one were to mesh a complex UNSTEADY geometry how much time would it take (roughly in terms of one computational timestep)? Note, meshing would have to be done every timestep, so we cannot amortize mesh generation cost over the simulation lifetime!

2) Mesh/grid adaptivity:

What is the computational complexity in this case?

Is adaptation faster or slower than mesh generation? How much is the cost per timestep compared to everything else? (say we want tolerance of 1.e-4 for vorticity)

Is it still true that (parallel) scalability is very poor for the poisson solution with adaptivity? or has the problem been solved?

What are the current issues with adaptation that need to be resolved?

Thanks in advance

Adrin Gharakhani