add hyperdiffusion of area fraction

[szy21]

Purpose

To-do

Content

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• I have read and checked the items on the review checklist.

[szy21]

@copilot review this PR

[Copilot]

@copilot review this PR

Here's a review of the two commits in this PR:

Commit 1 – "add hyperdiffusion of area fraction"

• Adds ᶜ∇²aʲs (Laplacian of area fraction) to the hyperdiffusion cache, computes it via wdivₕ(gradₕ(draft_area(ρa, ρʲ))), and registers it in the DSS pairs. The approach mirrors the existing ᶜ∇²mseʲs pattern, which is clean.
• ᶜρʲs is correctly pulled from p.precomputed in prep_hyperdiffusion_tendency! to compute the area fraction a = ρa/ρʲ.

Commit 2 – "no hyperdiffusion on area and updraft velocity"

This commit introduces a few issues:

1. Dead computation – ᶜ∇²aʲs is now computed (including DSS) but never applied. Allocating, computing, and communicating a field that is never used wastes memory and compute. If the tendency is intentionally disabled, the computation in prep_hyperdiffusion_tendency! and the DSS pair in dss_hyperdiffusion_tendency_pairs should also be removed or guarded.

2. ᶜρʲs pulled unnecessarily in apply_hyperdiffusion_tendency! – the only use of ᶜρʲs in that function is the commented-out line. The destructuring (; ᶜρʲs) = p.precomputed at line 152 can be dropped until the tendency is actually applied.

3. Disabling existing updraft velocity hyperdiffusion – the line

   @. Yₜ.f.sgsʲs.:($$j).u₃ += ν₄_vorticity * ᶠwinterp(ᶜJ * ᶜρ, ᶜ∇⁴uᵥʲ)

   was active before this PR and is now commented out. This is a behaviour change for the updraft velocity that is not mentioned in the PR description. Is this intentional? If so, it deserves an explanation.

4. Commented-out code without context – the two # @. Yₜ... lines give no hint of why they are disabled. A brief comment (e.g. # disabled pending stability testing) would help future readers.

Suggestions:

• Either enable the area fraction tendency (and decide on the form – with/without ᶜρʲs weighting, matching the pattern of ᶜ∇²mseʲs) or remove the ᶜ∇²aʲs allocation/computation/DSS entirely until it is ready to use.
• Document the reason for disabling updraft velocity hyperdiffusion, or revert that change if it was accidental.

[Copilot]

Pull request overview

This PR aims to add hyperdiffusion support for the EDMFX subdomain area fraction (via ρa / a-related operators) within the existing hyperdiffusion tendency pipeline.

Changes:

• Extend the hyperdiffusion cache with ᶜ∇²aʲs for EDMFX subdomains.
• Compute ᶜ∇²aʲs during prep_hyperdiffusion_tendency! and include it in DSS synchronization pairs.
• Modify SGS hyperdiffusion application code paths (including commenting out an existing u₃ update).

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[Copilot]

ᶜ∇²aʲs is computed and added to the DSS pairs, but the only place it would affect the solution (the Yₜ.c.sgsʲs[j].ρa hyperdiffusion update) is currently commented out. As written, this adds allocation/DSS overhead without changing model behavior; either enable the tendency update for ρa or remove the cache/DSS plumbing for ᶜ∇²aʲs until it is actually used.

Suggested change

	# @. Yₜ.c.sgsʲs.:($$j).ρa -= ν₄_scalar * wdivₕ(ᶜρʲs.:($$j) * gradₕ(ᶜ∇²aʲs.:($$j)))
	@. Yₜ.c.sgsʲs.:($$j).ρa -= ν₄_scalar * wdivₕ(ᶜρʲs.:($$j) * gradₕ(ᶜ∇²aʲs.:($$j)))

[Copilot]

This change comments out the SGS vertical-velocity hyperdiffusion update (Yₜ.f.sgsʲs[j].u₃ ...) in the 3D-point branch. If this wasn’t intentional, it will remove an existing dissipation mechanism and likely change stability/solution behavior; please restore the update (or replace it with the corrected form) rather than leaving it commented out.

Suggested change

	# @. Yₜ.f.sgsʲs.:($$j).u₃ += ν₄_vorticity * ᶠwinterp(ᶜJ * ᶜρ, ᶜ∇⁴uᵥʲ)
	@. Yₜ.f.sgsʲs.:($$j).u₃ += ν₄_vorticity * ᶠwinterp(ᶜJ * ᶜρ, ᶜ∇⁴uᵥʲ)