This note records the scientific and code provenance of the UAWSoM extension before it is integrated into the MHD module. The scientific authority is McMurdo et al. (2026), A&A 705, A15, doi:10.1051/0004-6361/202555912. The compatibility reference is commit 932ee5d of maxmcmurdo/Solar_MHD_2026_tutorial_UAWSoM_in_MPIAMRVAC.

Deliberate differences from the tutorial fork

The total-energy flux follows Eqs. 4–7 directly. Because the conserved total energy already contains the four wave energies, only the wave-pressure work and field-aligned propagation parts are added to the ordinary MHD energy flux. The tutorial fork adds the complete wave flux a second time and therefore duplicates its bulk-velocity part.

The kink expansion-work source follows the positive right-hand-side sign in paper Eq. 4. The tutorial fork applies this term with the opposite sign; that fork behavior is not retained.

The tutorial fork hard-codes the second coordinate, solar radius, filling factor, thread radius, reference field, and correlation lengths. The merged version uses Cartesian dimension-independent operators and runtime parameters. A user callback can provide local density contrast, thread radius, and Alfven correlation length. The supplied solar-atmosphere example implements the paper profiles through that callback.

The solar-atmosphere test follows the paper configuration: zeta0=5, B0=20 G, and R0=1 Mm. It returns Eq. 30's zeta=1+(zeta0-1) exp(-z/(5 R_sun)), Eq. 29's magnetic expansion of the thread radius, and the temperature-dependent closure stated after Eq. 9, Lperp_AW=1e8 sqrt(T_MK/B_G) m. The callback receives whether its state is primitive or conserved so that both solver paths evaluate the same physical temperature. The fork's base zeta=6, R0=0.1 Mm, and temperature-independent Alfvén correlation length are not retained.

Reflection and propagation conventions

MPI-AMRVAC labels wAplus and wkplus as the populations propagating against the local magnetic field, while wAminus and wkminus propagate along it. In a B0-split run every reflection speed uses the total field B = B_perturbation + B0, not the perturbation alone. Define

b = B/|B|, v_A = |B|/sqrt(rho), and v_k = |B|/sqrt(rho_e (zeta+1)/2), with rho_e = rho/(1 + f zeta - f). The Cartesian gradient/vorticity closure uses

S_A = v_A b dot grad(ln v_A), Omega_A = b dot curl(v), and S_k = v_k b dot grad(ln v_k).

The Alfvén reflection limiter is bounded by the larger nonlinear Alfvén damping rate, R_imb,A = sqrt(S_A^2 + Omega_A^2) and R_lim,A = min(R_imb,A, max(Gamma_plus, Gamma_minus)). Kink reflection uses R_lim,k = min(abs(S_k), max(Gamma_kplus, Gamma_kminus)); it deliberately omits Omega_A. Neither multidimensional limiter contains mhd_uawsom_sigma. The 4:1 population-imbalance factor is zero between the two 4:1 thresholds, and approaches a bounded signed value for stronger imbalance. For W_plus >= 4 W_minus, F = 1 - 2 sqrt(W_minus/W_plus) >= 0; therefore a positive exchange T = R F sqrt(W_plus W_minus) removes energy from the plus population and adds the same amount to the minus population. For W_minus >= 4 W_plus, F <= 0, so the updates reverse and weaken the minus population. Between the thresholds F=0. Thus the helper always weakens the dominant population, enhances the minor population, and leaves balanced states unchanged. The donor cap abs(T) <= W_donor/dt uses the actual post-damping donor state; the equal-and-opposite updates conserve the exchanged wave energy without silently repairing a negative state produced by the ordinary sources.

‘mhd_uawsom_reflection_mode='one_dimensional_gradient’retains the original one-dimensional gradient source and its sign convention; only this path uses the positivemhd_uawsom_sigmamultiplier. The default remains one_dimensional_gradientfor backward compatibility. cartesian_gradient_vorticityis the multidimensional Cartesian gradient/vorticity closure and runs whenever Alfvén reflection is enabled, including withmhd_uawsom_sigma=0.mhd_uawsom_kink_reflection=.true.` enables the kink-speed-gradient exchange independently of both the Alfvén switch and sigma.

The kink expansion-work source is the positive right-hand-side term in paper Eq. 4: +(zeta-1)/(zeta+1) p_k div(v) in the gas-energy equation. Its sign is independent of the reflection exchange.

Supported scope

The implementation supports uniform Cartesian 1D, 2D/2.5D, and 3D total-energy MHD with the fixed-ionization EOS, including B0 splitting. The current task intentionally does not implement cylindrical, polar, or spherical coordinates; semirelativistic, internal-energy, or hydrodynamic-energy formulations; FLD; nonuniform grids; or angular-momentum fix, source_geom/source_geom_split, or angmomfix combinations.

Before upstream merge, this table and the two explicitly recorded tutorial differences (energy-flux double counting and kink-work sign) are the author confirmation checklist.