Some initial questions on `1D notebook`

dhruvbhagtani / toy-model

This is a hybrid model of the global ocean with simplified governing equations to understand large scale circulations.

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Some initial questions on `1D notebook` #3

Open navidcy opened 3 years ago

navidcy commented 3 years ago

In the 1D Notebook:

I can't see any comparisons with analytic solutions (although the markdown comments claim so)

From the chat in Slack I understood that @dhruvbhagtani2105 and @AndyHoggANU agreed using periodic boundary conditions for these 1D tests. However:

I can’t see how we impose periodic boundary conditions.
We should make sure you get the convergence your scheme implies. That is we should integrate up to a fixed time t and check that the difference from the numerical and analytical solution diminishes as dt^p and as dx^q when you vary dt and dx respectively. (p and q being the order of your temporal and spatial scheme).

cc @AndyHoggANU

AndyHoggANU commented 3 years ago

To use periodic BCs, don't you just need a full sinusoid in the domain, and then amend the BCs? At the moment, the advection is advection in the BC from the left hand edge, which is not ideal. Why do you say that BC's can't be periodic?

navidcy commented 3 years ago

To use periodic BCs, don't you just need a full sinusoid in the domain, and then amend the BCs? At the moment, the advection is advection in the BC from the left hand edge, which is not ideal. Why do you say that BC's can't be periodic?

I didn’t say they can’t be periodic. I iust said that I don’t see how Druv is imposing periodic boundary conditions. But I simply may have missed it.

AndyHoggANU commented 3 years ago

Oh, sorry, I thought you were saying it couldn't be done...

dhruvbhagtani commented 3 years ago

@navidcy presently in the notebook there are no periodic boundary conditions, it was what I planned on doing. @AndyHoggANU you're right, I would need a full sine wave to be able to apply periodic boundary conditions.

navidcy commented 3 years ago

I don’t understand why a full sin wave is needed to apply periodic bcs. Periodic bcs can be applied regardless of the initial condition/actual solution. I don’t understand your remark @dhruvbhagtani2105 or I disagree with @AndyHoggANU if he made such statement and mislead you.

dhruvbhagtani commented 3 years ago

Hi Navid - yes, you're correct. We were talking in the context of a sine wave only. My statement was misleading, theoretically, we can have any function and impose periodic boundary conditions, as long as the function is periodic.