Semi-Lagrangian trace-back is unit-inconsistent under active units (dt not dimensionalised in has_units path)

[lmoresi]

Summary

With the units system active (unit-bearing mesh/variables), NavierStokesSLCN / AdvDiffusionSLCN fail in the semi-Lagrangian trace-back:

ValueError: Cannot subtract arrays with incompatible units: 'meter' and 'meter / second'

Root cause

SemiLagrangian.update_pre_solve computes the trace-back midpoint (src/underworld3/systems/ddt.py:2651):

mid_pt_coords = coords - v_at_node_pts * (0.5 * dt_for_calc)

In the has_units branch, coords is UnitAwareArray[meter] and v_at_node_pts is [meter/second], but dt_for_calc is left as a plain (dimensionless) float (ddt.py:2519):

if has_units:
    if hasattr(dt, "to"):
        dt_for_calc = dt.to("second")
    else:
        dt_for_calc = dt          # comment says 'treat as seconds' but leaves it unitless

so v[m/s] * dt[dimensionless] = [m/s] and the subtraction [m] - [m/s] raises.

Naively attaching seconds would fix the units but be numerically wrong: a CFL dt computed in nondimensional model-time is not SI seconds — it must be reconciled with the dimensional coords/velocity via the model time-scale. The sibling not has_units branch already does the consistent thing (nondimensionalise coords, velocity and dt together).

Fix direction

Make the units-active trace-back internally consistent — either dimensionalise dt to seconds via the model time-scale in the has_units path, or (cleaner) always perform the trace-back nondimensionally (strip units from coords/velocity/dt together, as the not has_units branch does) regardless of has_units.

Reproduction

docs/examples/Tutorial_Thermal_Convection_Units.py (PR #263) reaches the time-stepping loop and fails here. That tutorial is the natural regression test once fixed.

Exposed by PR #263 (held pending this fix).

Underworld development team with AI support from Claude Code

[lmoresi]

Fixed by #277 (merged to development). The SL trace-back now runs entirely in ND/DM space regardless of units; verified units-active AdvDiffusionSLCN runs and matches the nondimensional run to ~1e-3 (regression test_1056). The remaining ~1e-3 is the constitutive diffusivity scaling under units — separate concern.