3. A blast on a static AMR grid

A 2-D blast on a grid with a refined patch: the AMR keys, what the refined grid looks like in the output, and the check that matters across 2:1 faces, conservation.

The case

src/tests/flume/regression/blast-amr-limiter/input.ini is the Balsara–Spicer magnetised blast: $\rho =1$, $p=0.1$ outside, $p=1000$ inside $r<0.1$ around $(0.5,0.5)$, $|\mathbf{B}|=100/\sqrt{4\pi }$ at 45° (ambient $\beta =2.5\cdot {10}^{-4}$), ideal MHD with EGLM cleaning, periodic in $x$ and $y$. It is a hard problem on purpose: the low $\beta$ drives the pressure negative unless the positivity limiter is on, which is the subject of the next page. Here it is the grid that matters.

The AMR keys

(Excerpt: the committed input also sets the marker's delta_type, delta_fine, delta_coarse, box_zmin and box_zmax, which the parser requires.)

[grid]
ni = 16
nj = 16
nk = 4             ; z is a null axis (null_z = .true.)

[amr]
max_level      = 3
ratio          = 8  ; octree
iu_ref_levels  = 2  ; two uniform levels: 64 blocks, 64 x 64 cells
markers_number = 1  ; one marker refines further
frequency      = 0  ; no runtime regridding

[amr_marker_1]
mode         = 1               ; geometric marker
geo_type     = primitive-box
box_xmin     = 0.55
box_ymin     = 0.55
box_xmax     = 0.7
box_ymax     = 0.7
target_level = 3               ; refine the blocks in the box up to level 3

[initial_conditions]
amr_iterations = 1             ; set the IC, refine, set the IC again on the new grid

A block is refined when its centroid lies in the box; the box selects the base block $[0.5,0.75{]}^2$, so two 2:1 faces cross the blast centre. Every refined axis needs an even block cell count of at least 2 ngc (AMR cookbook).

Run it

mpirun -np 2 ../../exe/adam_flume_cpu input.ini > log.txt

The case stops after it_max = 100 steps, at $t=2.604\cdot {10}^{-3}$. Counting the blocks of the field files, step 0 and step 100 both hold 92 blocks with two spacings, $\mathrm{\Delta }x=1/64$ and $1/128$: the 4 blocks of the box column (the null $z$ axis keeps 4 copies) became 32.

In ParaView, colour by r and switch the representation to Surface With Edges: the refined patch shows as blocks of half the cell size.

The check: conservation across the 2:1 faces

blast-amr-limiter-conservation_history.dat, first and last rows, the mass column:

VARIABLES="it" "time" "int_r" ...
0   0.0000000000000000E+000 1.0000000000000000E+000
100 2.6041666666666683E-003 9.9999999999999967E-001

On a periodic box the mass is conserved exactly by the scheme, and it is here to $3\cdot {10}^{-16}$ although the blast crosses the 2:1 faces: at the end of each step the reflux replaces the coarse face flux with the sum of the fine ones, so both sides exchange the same flux. The AMR conservation page checks the same property on a dedicated case, and the positivity limiter page (PV-5) runs the same blast to $t=0.01$ on a different refined region, $[0.25,0.75{]}^2$.

What you learned

• Static refinement is max_level, a marker section and amr_iterations; frequency = 0 keeps the grid fixed.
• The output holds every block at its own spacing; counting blocks and spacings is the quickest check of the grid.
• Across 2:1 faces the reflux keeps the scheme conservative; the conservation history shows it.

Previous: 2. Lax. Next: 4. The positivity limiter.