6. Analysis and Output

Fluctuating-hydrodynamics results are statistical, so most analysis happens while the simulation runs: FHDeX accumulates means, variances and spectra over many time steps and writes them alongside the instantaneous fields.

6.1. Plotfiles

All applications write AMReX plotfiles (Plotfile) every plot_int steps, named <plot_base_name><step> with plot_base_name defaulting to plt. Staggered (face-centred) fields are written to separate plotfiles (stagx, stagy, stagz) when plot_stag = 1. Particle applications add particle plotfiles; see the application pages for the exact names.

Plotfiles can be read by VisIt, ParaView, yt and AMReX’s amrvis (VisIt), and compared with the AMReX post-processing tools (Post-Processing).

6.2. Structure factors

The static structure factor \(S(\mathbf{k}) = \langle \hat{\delta a}(\mathbf{k})\,\hat{\delta b}^*(\mathbf{k}) \rangle\) measures the spectrum of fluctuations and is the main diagnostic for verifying fluctuating-hydrodynamics solvers against theory. The StructFact class in src_analysis computes it with FFTs:

StructFact structFact;
// var_names: one name per field; var_scaling: normalisation per pair
structFact.define(ba, dmap, var_names, var_scaling);
// or only selected pairs (a_i, b_i):
structFact.define(ba, dmap, var_names, var_scaling, s_pairA, s_pairB);

// every struct_fact_int steps after n_steps_skip:
structFact.FortStructure(fields);        // add one sample
structFact.WritePlotFile(step, time, "plt_SF");

Each call to FortStructure adds one snapshot to a running average. By default, the class computes all auto- and cross-correlations of the variables (\(N(N+1)/2\) pairs for \(N\) variables), and var_scaling must have one entry per pair. WritePlotFile writes two plotfiles, <name>_mag<step> (magnitude) and <name>_real_imag<step> (real and imaginary parts), with the zero wavenumber shifted to the centre of the domain.

The relevant inputs are struct_fact_int (sampling interval; <= 0 disables structure factors) and n_steps_skip (equilibration steps to skip before sampling). Some applications also compute structure factors of quantities averaged along one direction (“flattened”, e.g. plt_SF_Flattened in exec/hydro), or in two slabs separated by cross_cell (do_slab_sf).

Turbulence spectra: IntegratekShells and the functions in TurbSpectra integrate spectra over spherical shells in wavenumber space and write the shell-averaged kinetic-energy and scalar spectra \(E(k)\) for turbulence studies.

6.3. Means, variances and correlations

src_common provides running statistics (ComputeBasicStats), spatial means and variances (ComputeSpatialMean, ComputeSpatialVariance) and plane averages (WriteHorizontalAverage). The compressible staggered solver writes means, variances, covariances and spatial correlations with the point cross_cell to its plotfiles, as selected by plot_means, plot_vars, plot_covars and plot_cross. Statistics are reset after n_steps_skip steps so that transients are excluded.

6.4. Checkpoint and restart

Checkpoints are written every chk_int steps to <chk_base_name><step> (default prefix chk). To restart, set restart to the step number of the checkpoint. Particle applications also use particle_restart. Some applications (e.g. exec/DSMC) discard the accumulated statistics on restart when reset_stats = 1. The hydro checkpoint also stores the random-number state of each MPI rank, so a restarted run continues the same random sequence.

6.5. Python tools

python/amrex_to_vtp.py: Reads AMReX particle output (plt*/particle0/Header and data files) and writes ParaView .vtp files.
python/write_pview_file.py: Helper functions for writing ParaView files (structured grids and particles), used by amrex_to_vtp.py.
python/convertSeries: Shell script that runs amrex_to_vtp.py on every parplt* particle plotfile of an exec/immersedIons run and collects the results as a numbered .vtp series for ParaView animation.

Several applications also include their own analysis scripts, e.g. exec/hydro/PDF and exec/compressible_stag/TURB_PDFS.