[WIP] Implement conservative WENO-5

[Iddingsite]

The current implementation of the WENO-5 advection algorithm is using the non-conservative form of the advection equation (V∂T∂x). We can implement the conservative form (∂(VT)∂x) using directly the velocities on the staggered grid (see for instance here).

Three good reasons to do that:

• No need to interpolate the velocities from the sides to the center anymore
• Makes no assumption on the divergence of V, so will be fully compatible with compressible flow
• Would be fully conservative for the quantity advected

The implementation is a simple addition: using directly the velocities of the staggered grid for the value of the fluxes after using WENO-5 to approximate the advected quantity on the sides .

I have added a boolean kwarg to WENO_advection!() to be able to use both the non-conservative and the conservative form, but I believe that the conservative form should be the default. That would be a breaking change, because the input velocities required would be by default the velocities on the sides as opposed to currently velocities on vertices.

I have currently a problem with the boundary conditions, but I think I am mostly there. @albert-de-montserrat, is there a helper function to get only the interior points of for instance stokes.V.Vx? Because of the ghost points, I have to add +1 to my indexes currently and it would be nice if it could work by default with velocity fields without ghost points.

Needs #339 to be merged before.

[Iddingsite]

Alright, I understand my problem. I forgot that T was defined on the vertices in geodynamics, so this approach will not work for temperature (without interpolating of course). It will only work for quantities at the center of the stencil (η, ρ, Compo..). So I don't think there is a big interest for JustRelax.

[Iddingsite]

Closing that one for now.

[albert-de-montserrat]

@Iddingsite can I close this PR?