Optimisation for steadystate flows
From Gerris
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Often, you're not particularly interested in how a flow or stream develops over time, but only how the constant flow behaves if it exists long enough to have all initial reactions and changes settled. While Gerris isn't optimised for such calculations, a few simplifications and speedups exist.
Getting rid of advection calculations
In a mailing list thread people agree, a steadystate solution at very low Reynolds numbers (Re << 1) behaves equally to a pure Stokes flow and advection terms are negligible. You can switch them off:
GfsAdvectionParams { scheme = none }
For an example, see the Couette flow test case.
To give the removal of advection evidence, I've run the example from An engineer's pipe flow with the viscosity of water (Re = 2485) and up to time t = 1.0 (with advection it "explodes" at about t = 1.49) with and without advection:
At a Reynolds number of 2485, there are big differences, as expected. The calculation time drops from 4500 seconds to 80 seconds, but this speedup is useless as results are plain wrong.
So I did again with a Reynolds number of 0.01 (by pipe diameter):
As you can easily spot looking at velocities, the difference is still very significant. Both pictures use the same color scaling.
The pressure difference inlet to outlet is about 22 (fluid domain dimension) without advection but 340 with advection. Unlike most other pictures of this geometry shown, the pressure scaling in 1 to 200 here.
It pretty much looks like advection is needed for all but extreme cases.
End the simulation when the state is steady
In the same mailing list thread, Stéphane Popinet shows how to stop simulation as soon as a steady state is reached. This optimisation won't decrease computing time of the simulation, but will end it automatically without watching you how the flow develops.
In your calculation script, remove the end time and insert an GfsEventStop. The result could look like this:
GfsTime { } GfsEventStop { istep = 1 } U 1e3 DU GfsOutputSimulation { start = end } result%2.2f.gfs

U
is the variable to watch. Variables other than velocity should work as well.  The number behind this is the threshold (difference to previous value) at which the simulation is stopped when reached.
 The
DU
is finally a new, optional variable where the current difference is put in.  The GfsOutputSimulation is used to save this last state for viewing and restarting.
You can also add an additional
GfsOutputScalarNorm { istep = 1 } stdout { v = DU }
to watch this variable and how the velocity changes get fewer and fewer from step to step.
With this optimisation the simulation stops at a fluid domain time of 7.8 or a CPU time of 540 seconds and the results should be within a 1% accuracy of what you can reach.
 Nota Bene: It's a simulation after all and if a simulation would fit reality within a 1% accuracy, this would be stunning.
 Caveat: As of version 1.1.2 (080113033605), this appears to work with the fullyimplicit solver (see below), only. Tests included the example on this page with and without advection.
Using a different solver
The third point Stéphane made in this thread belongs to the type of solver. He writes:
 Also for Stokes flows, you probably want to use the fullyimplicit diffusion solver to avoid potential oscillations in time in the solution which can appear when using the default CrankNicholson diffusion solver. This decreases the timeaccuracy from secondorder to firstorder but it doesn't matter since you are looking for a steady solution.
Lacking time accuracy should have no influence on steadystate flows of higher Reynolds numbers either. Again, it's a simple change. Add a beta = 1
term to your GfsSourceViscosity
line, e.g.:
GfsSourceViscosity 4.024e5 { beta = 1 }
For comparison, I've run my favourite example with a Reynolds number of 2485 (water at 0.5 m/s) with both solvers:
Wall clock time needed for the calculation is the same within few seconds (of about 4500 seconds). Results are the same within 2% accuracy. The timeaccurate version appears to have a slightly lower Reynolds number.
It looks like the fully implicit solver doesn't change anything in normal situations. Nonetheless, it might help in some border cases.