GLM damping length on a seam

ID	Group	Milestone	Backends	Figure	Regression
G2	Seam studies	M6 (#68)	FNL only	yes	—

Case and scope

The GLM damping rate is $c_h^2/c_p^2=\alpha c_h/L$ with [mhd] glm_damping_length $L$ a fixed length or min-cell (the finest spacing; with runtime AMR it is frozen at the spacing of max_level, D-M5-9). A per-level length, each level damping at its own spacing, does not exist. G2 asks whether it would matter, bracketing it between the coarse and the finest spacings on A2's source-free CPAW.

Models and numerics

Item	Choice	Code
Equations	ideal MHD with mixed GLM, $\gamma =5/3$, glm_ch 2.0, glm_alpha 0.18	models
Damping length	glm_damping_length = 1.0, the coarse spacing $L_x/N$, or min-cell	set_glm_damping, adam_flume_mhd_object.F90
Space, time	WENO5 flux splitting on characteristic variables; SSP Runge–Kutta 5 stages, CFL 0.4	as in AD
Seam operators	mean + tricubic, reflux on	numerics
D_flux	the seam floor of [diagnostics] divb_flux	compute_dflux_norms, adam_flume_fnl_object.F90

Initial and boundary conditions

Item	Value
Case	the cpaw leg of AD: source-free CPAW, $[0,\sqrt{5}]\times [0,\sqrt{5}/2]$, quadtree, two $x$ seams ($x\in [0.6,1.6]$ refined)
Grid	refined and uniform $N$ = 64 / 128
Boundaries	periodic in $x$, $y$; extrapolation in $z$
Final time	10 periods
Ranks	2, FNL

Input files

File	Role
src/tests/flume/verification/amr-divb/make_amr_divb.py cpaw	the CPAW inputs (--glm-damping-length: 1.0, the coarse spacing, min-cell)
src/tests/flume/verification/amr-divb/amr_divb_oracle.py growth	the seam floor and its growth
src/tests/flume/verification/make_doc_runs.sh <runs> divb (FNL), make_doc_figures.py --only glm-damping	re-runs the CPAW with the coarse spacing and min-cell (--glm-damping-length), $N=64$ and 128; the 1.0 runs are those of AD

Results

FNL: the seam maximum of D_flux on the source-free CPAW for the three damping lengths, refined $N=64$ and 128. The re-runs reproduce the table below (the medians of the second half): every length bounded, min-cell doubling the floor at $N=128$.

glm_damping_length	rate $c_h^2/c_p^2$ (N = 128)	seam D_flux floor N = 64 / 128	× uniform (N = 128)	growth N = 128
1.0 (A2)	0.36	$5.39\cdot {10}^{-4}$ / $5.43\cdot {10}^{-5}$	119	0.72
coarse spacing $L_x/N$	20.6	$6.96\cdot {10}^{-4}$ / $5.32\cdot {10}^{-5}$	116	1.02
min-cell (finest spacing)	41.2	$8.30\cdot {10}^{-4}$ / $1.07\cdot {10}^{-4}$	233	1.01

Related cases: AD is the A2 baseline (first row); the uniform-grid cleaning is GLM divergence cleaning.

Findings

• Every length keeps the seam divergence bounded (growth 0.72 to 1.02 over 10 periods).
• Strong damping raises the seam floor: min-cell doubles it at $N=128$ against the coarse spacing or the domain-scale length; a per-level length (between the coarse and the finest spacings) would sit between them.
• The D-M5-9 freeze stays (the plan's choice): its cost on this test is at most that factor 2 on the floor, with the damping rate fixed through regrids. No per-level option is added.