4.1. Diagnostic Output

4.1.1. Global quantities

To provide information on the progress of execution, a number of fluid quanities are summarised to standard output at a frequency determined by

freq_statistics    1000

Here the frequency would be once every 1000 time steps. Note that these global statistics require collective communication and can be relatively expensive to compute (compared with a single time step).

The details of the exact global statistics produced depends upon the choice of free energy, and the presence of other features in the particular simulation. All output is reported in lattice units.

4.1.2. Diagnostic examples Fluid-only system

For fluid only problems, the global sum, mean and variance, minimum and maximum of the scalar density field are reported. For free energy cases, corresponding order parameter statistics are included, e.g. for a binary fluid case with compositional order \(\phi\), we might have:

Scalars - total mean variance min max
[rho]      262144.00  1.00000000000  1.5449642e-11  0.99998006808  1.00001625877
[phi]  3.1484764e+00  1.2010484e-05  3.7820523e-04 -4.7270149e-02  4.6821679e-02

Here the total density reported against [rho] should be \(\rho_0\) per fluid site (the total fluid volume for the system in the case that \(\rho_0\) is unity). Maximum and minimum density should alert the user to any significant deviation from the Mach number constraint which means that the density should be close to \(\rho_0\) throughout the fluid. The same statistics are reported for compositional order [phi]. Net composition should not change for a conserved order parameter, so the total reported for [phi] should be fixed after initialisation (see further comments below). The maximumm and minimum order parameter may extend slightly beyond the equilibrium values \(\pm \phi^\star\).

The total free energy is reported:

Free energy density - timestep total fluid
[fed]             10 -9.7510518349e-07 -9.7510518349e-07

The exact format of the report again depends on the choice of free energy and simulation details, but in this example gives the total integrated over all fluid sites in a fluid only system (the fluid contribution and the total being identical).

The total fluid momentum is reported in each coordinate direction:

Momentum - x y z
[total   ]  3.6427701e-12 -1.5761698e-14 -4.5102810e-15
[fluid   ]  3.6427701e-12 -1.5761698e-14 -4.5102810e-15

If initialised with a fluid at rest, the total momentum should be zero (to within machine precision of around \(10^{-16}\)). In the absence of external forces, the total momentum should be conserved. However, in practice, the figures reported will drift owing to the accumulation of round offs errors (as seen in the above example). However, these errors should remain small compared with unity.

The total momentum from the fluid is computed as a compensated sum, so should be robust to parallel decomposition. Other contributions to the total momumtum (e.g., from colloids) are not currently treated in the same way. Conserved order parameter

In cases where composition is locally and globally conserved (as in the symmretic binary fluid), some care can be taken to ensure the total reported order parameter (ie., the composition) remains fixed as a function of time. There are at least two sources of round-off error that can lead to apparent drift in the total reported as

Scalars - total mean variance min max
[rho] ...
[phi]  3.1484764e+00  1.2010484e-05  3.7820523e-04 -4.7270149e-02  4.6821679e-02

The first is in the evaluation of the total itself (and particularly the order in which the sum is accumulated in parallel). This is handled in all cases via a compensated sum, which should ensure the results are consistent independent of parallel decomposition (in both MPI/thread sense). The second is the time evolution via the Cahn-Hilliard equation. Additional measures can be taken if required here via the option:

cahn_hilliard_options_conserve  1   # integer value 0, 1, or 2

The choices are 0 (the default) which means no special action; 1, which indroduces an additional compensation at each point of the lattice in the Cahn Hilliard update; and 2, which introduces a post-hoc correction to maintain the initial value of the total order parameter at each time step. These options may be of interest if strict conservation at machine precision is wanted. This may be most noticeable if the total is exactly zero or very close to zero. For most purposes, the default should be acceptable.

4.1.3. Timing and performance

Timing for various parts of the code is produced at the end of a normal run.

In addition, the following options are available:

timer_lap_report          yes        # request lap timer [optional]
timer_lap_report_freq     1000       # every so many steps

This option produces a “lap” time every so many steps, i.e., the elapsed wall clock time since the previous lap (or since the start of execution for the first lap). If the option is selected a non-zero timer_lap_report_freq must be provided. The lap report is not provided by default.

A lap report will be to standard output, and is of the form:

Lap time at step   1000 is:  8.683 seconds at Thu Dec 23 14:23:04 2021
Lap time at step   2000 is:  8.521 seconds at Thu Dec 23 14:23:13 2021

showing a lap time of something over 8 seconds.