Fix overwritten axisymmetric Jacobian in the SST source

[Syphonicc]

Title: Fix overwritten axisymmetric Jacobian in the SST source

Proposed Changes

In CSourcePieceWise_TurbSST::ComputeResidual, ResidualAxisymmetricConvectionDiffusion subtracts its
contribution from the diagonal of Jacobian_i, but the "Implicit part" right after it assigns
Jacobian_i[i][j] = ..., so that contribution was always discarded.

This PR:

• calls the axisymmetric function after the implicit block, so its Jacobian contribution is kept;
• uses the derivative w.r.t. the conservative variables (rho k, rho w), yinv * Volume * v (the previous
  dead code had yinv * Volume * rho * v);
• keeps only the part that increases diagonal dominance, max(v, 0). With both signs of v, the term is
  destabilizing for flow towards the axis: on air_nozzle_restart it stalls at rms[Rho] ~ -5.6, instead of
  reaching -12 in 591 iterations.

Residuals are unchanged; only the convergence path differs, so the air_nozzle regression values are
updated. Results on air_nozzle_restart, a pipe with radial injection from a central rod, and an impinging
round jet show no change in convergence (see the discussion below).

Related Work

#2948 edits the same implicit block of the SST source.

PR Checklist

• I am submitting my contribution to the develop branch.
• My contribution generates no new compiler warnings (try with --warnlevel=3 when using meson).
• My contribution is commented and consistent with SU2 style (https://su2code.github.io/docs_v7/Style-Guide/).
• I used the pre-commit hook to prevent dirty commits and used pre-commit run --all to format old commits.
• I have added a test case that demonstrates my contribution, if necessary.
• I have updated appropriate documentation (Tutorials, Docs Page, config_template.cpp), if necessary.

[bigfooted]

Since it does not harm the current case, and it is expected to help in certain other cases, I think the better approach is to keep the correct term with max(v,0).
An example testcase where this Jacobian would help is a pipe flow with a central rod that injects flow radially through a permeable (or perforated) wall. This is actually a pretty common setup. Do you have setups where there is a dominant radial velocity present close to the axisymmetry?

[Syphonicc]

Thanks, makes sense. I've switched to keeping the exact derivative w.r.t. (rho k, rho w), yinv * Volume * max(v, 0), with the axisymmetric call moved after the implicit block so it is not overwritten. The air_nozzle regression values are updated (serial and MPI; I'll take the hybrid ones from CI since I don't have an OpenMP build).

I didn't have a case with dominant radial velocity near the axis, so I set up two (incompressible SST, 4000 iterations, fixed CFL, before = develop, after = this PR):

Pipe with a central rod (r0 = 5 mm, R = 50 mm) injecting radially at 5 m/s through a permeable section. Iterations to rms[P] = -11:

CFL	develop	this PR
20	not reached (-9.91)	not reached (-9.91)
100	930	930
500	208	211
1000	165	165

Round jet impinging on a plate (H/D = 2, Re = 23000). rms[P] / rms[k] after 4000 iterations:

CFL	develop	this PR
20	-5.35 / -3.37	-5.35 / -3.37
100	-9.44 / -7.52	-9.44 / -7.52
500	-8.15 / -7.34	-8.15 / -7.33
1000	-7.20 / -6.90	-7.22 / -6.90

So no harm, but also no measurable benefit in these two. I think the reason is that, since the axisymmetric volume is the planar cell area, the term relative to the convective Jacobian is about dy/y. Away from the axis (rod surface, first cell 1e-5 m at r = 5 mm) that's ~0.002. Next to the axis it tends to Volume * dv/dr, which is small compared to the beta* omega Volume dissipation entry. Happy to add one of these as a regression case if it's useful.