Should we enforce dealiasing before any calculation of nonlinear terms?

[navidcy]

I think we should be applying dealias!(sol, prob.grid) before any calculations of quadratic nonlinearities. We were getting away with this up to now either because of viscosity/hyperviscosity damping high-wavenumber modes or due to the Filtered time steppers.

[glwagner]

I think it should be user choice, but this is a good default.

[navidcy]

Well I don't understand exactly what you may be implying.

Also, e.g., if a user wants to solve 2D Navier-Stokes with advection terms like u ∂ζ/∂y + v ∂ζ/∂x they should be, in principle, able to do it. But they will have to write their own module...

I'm just saying that modules should solve the right equations and, of course, if a user wants to do something else they can do it. The modules claim that they compute nonlinear quadratic terms but they have aliasing error if sol is not dealiased properly, don't they? So I'm only suggesting we make the modules compute what they claim to compute (within the limits of their resolution restrictions).

[glwagner]

So I'm only suggesting we make the modules compute what they claim to compute

Can you be more specific? Do we claim that we dealias nonlinear products?

[navidcy]

No, we "claim" that modules compute, e.g., u*ζ, and derivatives of this. But in fact, it computes u*ζ+aliasing errors due to the finite resolution of the grid. Right?

[glwagner]

We compute a numerical approximation to u*ζ which contains both aliasing errors (if not dealiased, and if there is non-zero power at aliased wavenumbers) and truncation errors (always).

[navidcy]

Yes. I was at some point mislead to think that if you have filter or hyper viscosity than there is no aliasing errors though. And I'm trying to avoid this situations for others.

[glwagner]

Heh, well many users will not run simulations with aliasing errors if dealiasing is default. I agree with that. I'm not sure anybody will be the wiser regarding an understanding of aliasing errors though.

One caveat is that the effective resolution of simulations with dealiasing is 2/3 or what's specified. So people will write nx=256 and not realize that their simulation in fact has a resolution of 192. That's one argument for requiring users to intentionally dealias.

Or you can go the way of dedalus and use 3/2 dealiasing. That's certainly the right way to do it if one needs to define a "right" way.