Pass the edge length, not its square, to the coarse NEMO viscous Jacobian

[bellonarts]

Proposed Changes

CAvgGrad_NEMO::ComputeResidual (SU2_CFD/src/numerics/NEMO/NEMO_diffusion.cpp) computes the edge vector between the two nodes and then assigns

dist_ij = GeometryToolbox::SquaredNorm(nDim, dist_ij_2);

before passing dist_ij to GetViscousProjJacs, which expects the distance, not its square. The corrected-gradient sibling in the same file already takes the square root (dist_ij = sqrt(dist_ij_2);). This PR applies the same square root in CAvgGrad_NEMO, a one-line change. The residual is untouched; only the analytic viscous Jacobian changes, by a factor of the edge length.

Where the defect is reached. CDriver.cpp instantiates CAvgGrad_NEMO for the interior viscous term (visc_term) on every multigrid level above the finest, and for the boundary viscous term (visc_bound_term) on every level including MESH_0. On MESH_0 the visc_bound_term numerics is consumed by only three boundary routines: CNEMOEulerSolver::BC_Far_Field, CNEMOEulerSolver::BC_Supersonic_Inlet and the inherited CFVMFlowSolverBase::BC_Fluid_Interface. The NEMO wall routines (BC_HeatFlux*, BC_Isothermal*, BC_Smoluchowski_Maxwell) assemble their own fluxes and never call it, and the viscous calls in BC_Inlet and BC_Outlet are commented out. So the defect reaches every NEMO Navier-Stokes run that uses multigrid, a far-field or supersonic-inlet marker, or a fluid interface, through the viscous Jacobian of those terms; a single-grid run whose markers are only walls, outlets and symmetry planes is untouched. The residual equations are unchanged; the corrected implicit operator changes the convergence path.

A unit test is added to UnitTests/SU2_CFD/numerics/CNumerics_tests.cpp: "NEMO coarse viscous Jacobian uses Euclidean edge length". It introduces a small NEMOViscousFixture (a 2-D AIR-5 edge from (0,0) to (3,4) with unit normal (0.6, 0.8), laminar viscosity 2, and a linear velocity gradient along the edge) and compares a central finite difference of the projected momentum flux against the analytic jacobian_i and jacobian_j returned by CAvgGrad_NEMO. The momentum block of GetViscousProjJacs is mu / d (theta I + n n^T / 3) with theta = |n|^2, so on this edge the analytic directional Jacobian must be -8/15 on the i side and +8/15 on the j side to 1e-12, and match the finite difference to 1e-8. Stock develop passes the squared length 25 in place of the distance 5 and returns 8/75, so the test fails there and passes with this change. The fixture, its helpers and the test case are commented in the source.

Regression effect (iteration 10, x86-64 Linux build of develop at 07aa46b). All three affected public cases use a MARKER_FAR boundary, which is how they meet the corrected Jacobian on a single grid. On the viscous cone (visc_cone, serial and parallel) and the super-catalytic wedge (super_cat, parallel) the columns that move are rms[Rho_2], rms[Rho_3] and rms[Rho_4], the three species that are identically zero in those cases (values near -20.5, the machine-zero floor); their physical columns match the same pod's stock run to the printed digits. The visc_cone hunks also carry shifts of at most 4e-6 in physical columns (serial rms[Rho_0] -5.215230 to -5.215233, CD 0.093206 to 0.093207; parallel -5.215234 to -5.215238, rms[RhoE] 1.262701 to 1.262697). Those are pod-versus-CI build noise, present in the pod's stock run as well, not an effect of this change; since SU2's regression harness compares the printed digits exactly, the final digits for these vectors are the ones this PR's CI prints. The ionized cylinder (ion_gy, parallel) is different: it has no identically-zero species, so its physical residual columns rms[Rho_0..5] and rms[RhoE] move by up to 1.05e-2 (for example rms[Rho_1] -4.165562 to -4.156741 and rms[Rho_2] -4.702662 to -4.692113), which is the expected footprint of a changed implicit operator on a converging case; its force, heat-flux and lift columns are unchanged. The expected vectors are rebaselined accordingly for visc_cone (serial and parallel), super_cat (parallel) and ion_gy (parallel). Every other NEMO regression case is unchanged. The final x86 digits are for this PR's CI to confirm, and the aarch64 vectors are left untouched for a maintainer since that workflow runs only on push to develop.

This source change is independently reviewable, but its visc_cone, super_cat, and ion_gy regression lines overlap the energy-under-relaxation and corrected-viscous-Jacobian PRs. These PRs should merge sequentially; whichever lands later must rebase and refresh the overlapping exact vectors from that PR's CI run.

Related Work

The NEMOViscousFixture added here is shared with a follow-up PR on the corrected-gradient NEMO viscous Jacobian (CAvgGradCorrected_NEMO, distinct left block and subtractive edge assembly), which will add only its own test case to the fixture; the PR number will be added here once it is opened. This change is also the prerequisite for any NEMO multigrid work, since the coarse-level interior viscous Jacobian is built exclusively by CAvgGrad_NEMO.

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[pcarruscag]

This looks like a good find, but just to be sure. Have you run two cases to convergence to further verify that this makes things better?

[pcarruscag]

I don't want tests that duplicate a ton of code to prove something that is trivial to prove correct by inspection. Make this substantially simpler or revert.

[pcarruscag]

We have a norm function