shallow water 1 layer, issues with gradient

[Aurélien Ponte]

Hi,

I am trying to build upon KleinGordon in order to setup a 1 layer shallow water model:
https://github.com/apatlpo/shenfun_trial/blob/master/swater_1L/swater_1L.py

Unfortunately, the time rate of change of variables is very small at the moment and I suspect I am not normalizing correctly terms corresponding to g\partial_x h.
In other terms, I am missing the A term in the KleinGordon example.

If anybody has an idea, I would be most grateful.

[Mikael Mortensen]

Hi
I had a quick look and I see two issues. One is as you mention, you are missing division by A in rhs terms that are not using forward, i.e., du_hat[:] = Cu*h_hat and dv_hat[:] = Cv*h_hat and dh_hat[:] = Chu*u_hat + Chv*v_hat. Note that forward here, with only Fourier bases, is just short for inner product divided by diagonal mass matrix, i.e., A. You can get A as A=inner(hh,hh_test) or simply A=(2*np.pi)**2. Second, you should expect min(du_hat) and min(dh_hat) to be zero, since these are in spectral space. What you ought to use is norms, like np.linalg.norm(u_hat).
Hope this helps.

[Aurélien Ponte]

Thanks a lot for this.
The principal bug was actually quite trivial (once spotted of course): line 174 was missing and messed up plotting.