Thanks @ChrisRackauckas and @dlfivefifty.
Is there a reason for a Pseudo Spectral method to be a good choice for the Shallow Water equations or is this only one of many choices?
I will be thankful for receiving a reference!
Everything in is one of many chances. But spectral methods tend to cope well with turbulence. For what it’s worth, the European Midrange Weather Forecast agency use a spherical harmonic code for their simulations.
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If your geometry and boundary conditions allow them, nothing beats the convergence rate of spectral methods.
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