Naming convention for fluxes

Currently we consider the flow of energy, mass or momentum as "fluxes" within the local residual classes, fluxVars, flux laws (e.g, Darcy and Fick), etc. However, they are actually absolute flows (e.g. in kg/s).

I know this is hairsplitting at its finest but my impression is that the literature commonly considers "fluxes" as "flow of some quantity per area" (such as kg/(sm²)). It also caused some confusion for me sometimes as I first have to look up if the multiplication with scvf.area() was already performed or not.

@all What is your opinion? Are there citable sources which actually do consider "fluxes" as something absolute? Should we bother to rename our stuff for sake of consistency?

added Discussion label

Thank you Kilian for bringing this up. I've also had this confusion about flux (flow rate) definition in dumux and it took time to get a used to it.

It is not citable, but the wikipedia article of flux https://en.wikipedia.org/wiki/Flux looks like it is generally a surface integral and then I think it would be fine the way we use the word.

I guess we use this definition https://en.wikipedia.org/wiki/Flux#Flux_as_a_surface_integral rather than this one https://en.wikipedia.org/wiki/Flux#Flux_as_flow_rate_per_unit_area.

From a language point of view I would say "flow" describes the phenomenon of moving fluid and "flux" is describing a quantity or the act of something flowing through something. (Also from wikipedia on the latin roots: "The word flux comes from Latin: fluxus means 'flow', and fluere is 'to flow'.") I would say it doesn't really matter if it's area-specific or not. That would be a matter of definition. But I'm not a language expert... In the same way a flow rate could be a mass flow rate, volume flow rate, or an area-specific mass flow rate, etc.. I think you should just always mention which unit you are referring too.

I found this article:

https://wikidiff.com/flow/flux#:~:text=As%20nouns%20the%20difference%20between,as%20of%20a%20flowing%20stream.

I didn't know there existed a diff Wiki :D. By gut feeling I would also have said that flow is rather fluid-specific and flux is more general. Whether or not it is per area or not is usually a matter of definition or sometimes handled by an adjective, isn't it? Like discharge vs specific discharge.

Long story short, I never had any issues with our choice of wording. And I would (out of the guts) think that using flow doesn't make it better.

I would agree with Dennis that something normalized in terms of some length, area or volume could be called specific quantity see Wikipedia. Especially from my thermodynamics courses I would expect a specific quantity to be normalized by some length, area or volume and German Wikipedia seems to agree. I don't know whether this is a very German definition though.

For users it would be convenient to have a better intuition of whether a quantity, e.g. a flux, is normalized in some way. However, I would definitely keep the term flux. To me the heat flux would be a common example that does not need to involve any flow or the fluxes in used in surface integrals as mention by Melanie.

I would personally welcome some change that makes it easy/easier to figure out if one has a 'absolute' flux or a normalized flux. Maybe it would also be possible to define the flux properly for DuMuX and document it properly such that it is easier to follow up on that? I would also support a proper terminology, but I guess for that you would still need to decide what the term will mean for DuMuX as people with different background might have different expectations. I would be fine with specificFlux for a flux normalized by area/length, for example, but this term is till not really descriptive in what sense the flux would be "specific".

TL;DR

My opinion:

• Use flux and not flow
• If you want to rename it, specify the meaning clearly and document it such that users find it.

To me the heat flux would be a common example that does not need to involve any flow or the fluxes in used in surface integrals as mention by Melanie.

The heat flux (and other fluxes) as used in dumux in the finite volume context is the surface integral exactly as mentioned by Melanie.

I agree with everything else.

I think if the documentation of a function states which unit the quantity has that is returned this should be unambiguous. For some more generic interfaces, e.g. Problem::neumann there is not only one unit because it depends on the equation we solve. But IIRC the documentation at least in that case clearly states that the you have to return a flux per surface area / area-specific flux (edit: at least it states the correct units in form of a mass balance example: https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/-/blob/master/dumux/common/fvproblem.hh#L274)

The flux function for box Fick's law is not documented: https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/-/blob/master/dumux/flux/box/fickslaw.hh#L86 I'll open an issue for that because it seems like an important function that deserved documentation especially in terms of units -> #905 (closed).

I agree with all of your points. I stumbled across this mostly due to a comment regarding the terminology in my thesis. It seems like the CFD community has a stronger preference for "flux" in terms of a relative quantity.

In the CFD community the term "numerical flux" is also often used in the context of Riemann problems (Euler equation, shallow water equations).

Just some remark, depending on the conservation law equations some of these fluxes are not equal on the left and right side of an interface between two cells. For example, applying some hydrostatic reconstruction methods for the shallow water equations may lead to a different momentum fluxes at the cell interface.

mentioned in issue #910 (closed)

mentioned in merge request !2221 (merged)

closed via merge request !2221 (merged)

mentioned in commit 7510e6cc