4. The positivity limiter

The blast of the previous page without the refined patch: run it without the limiter and see it fail, then with it and see it reach the final time.

The case

src/tests/flume/regression/blast-limiter/input.ini is the same Balsara–Spicer blast on the uniform $64\times 64$ grid (a quadtree: ratio = 4, nk = 1). Two changes to the copied input run it to the end instead of the regression's 100 steps, and select the limiter:

[numerics]
positivity_limiter = none     ; then: cell

[time]
it_max   = -1                 ; was 100: run to time_max
time_max = 0.01

The [mhd] floors are off (rho_floor = 0.0, p_floor = 0.0), so nothing hides a negative pressure.

Without the limiter

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

[mpi-00000]error stop : +4 cells with a non-positive density or pressure at step +3 (min rho +0.72590331193952229E+000, min p -0.15378822578668403E-002); the [mhd] floors rho_floor, p_floor are disabled

At $\beta =2.5\cdot {10}^{-4}$ the pressure is a tiny difference of large energies, and the high-order update makes it negative in the third step. FLUME stops rather than continue with a non-physical state.

With the limiter

positivity_limiter = cell blends every face flux of a cell with the first-order Lax–Friedrichs flux, just enough to keep the cell's density and pressure above a fraction (POSITIVITY_LIMITER_KAPPA = 0.1) of their first-order update. The same input with cell:

+193 +0.99908507877250665E-002 +8 ...       (the last row of blast-limiter-residuals.dat)

It reaches $t=0.01$ in 193 steps (the row shows the time at the start of the last step). The limiter changes only the cells where the high-order update would leave the admissible set; elsewhere the scheme is unchanged. The positivity limiter page runs this blast at ${128}^2$ with figures, its 3-D and AMR versions, and the near-vacuum tests.

What you learned

• FLUME stops on a non-positive density or pressure unless floors are set; it never continues silently.
• positivity_limiter = cell keeps the update admissible by blending with the first-order flux, cell by cell.
• The regression cases are small, complete inputs: copy one, change two keys, and you have a new experiment.

Previous: 3. A blast on a static AMR grid. This is the end of the FLUME track; the build-your-own-solver track shows how such an application is built.