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14 votes

Constructing random divergence-free velocity fields

Create two random scalar fields $f$ and $g$ and set the velocity to: $$ u=\nabla f \times \nabla g $$ which is guaranteed to be divergence free.
Bill Barth's user avatar
  • 10.9k
7 votes

Constructing random divergence-free velocity fields

A purely random initial condition will not resemble realistic turbulence and will take quite some time to reach a realistic decay state. If you want good results it's more complicated than just ...
Doug Lipinski's user avatar
4 votes

What is the best cooling and flippling schedule in simulated annealing?

It is very much problem dependent. The issue with going from Monte Carlo to Simulated Annealing to Very Fast Simulated Annealing is that one increases the number of tuning parameters that the method ...
Wolfgang Bangerth's user avatar
2 votes

Constructing random divergence-free velocity fields

If you are in 2D and if you want more physical setups, I suggest you consider potential flows. There are various ways to construct these potential flows which are always divergence free and which ...
Jan's user avatar
  • 3,418
2 votes

Quick way to find a common basis of eigenvectors between 2 matrices : valid or not?

Yes, the eigenvectors found with this method may depend on $x$ and $y$, but no, it doesn't matter in practice. If $A$ and $B$ share a basis of common eigenvectors, then $$ A = V\operatorname{diag}(\...
Federico Poloni's user avatar
1 vote

Multiscale Simulation of random walker

In general, the only harm a small step size causes is that it costs runtime. Therefore the step size imposed by your small random walkers is a reasonable choice. The only reason why it wouldn’t be is ...
Wrzlprmft's user avatar
  • 2,117

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