The computation of the diffusivity converges when the number of particles and the simulated time .

If the default mode Auto Distance, Check Convergence is chosen, the simulation time is iteratively increased until convergence is achieved.

If Fixed Distance is chosen, the convergence for is not checked, and a fixed simulation time is chosen. In this case, you have to enter the Average Travel Distance, which also fixes the simulation time . A distance is entered instead of a time value here, because the simulation runs with a dimensionless particle velocity. The mean thermal velocity of the diffusing particles is set during post-processing, and the results can be rescaled without the need to recompute the random walks.

If Suggest is clicked, GeoDict suggests a value for the average travel distance.

Select either Tolerance or a fixed Number of Random Walks.

With Tolerance, the solver stops if the relative standard deviation of the diagonal entries of the resulting diffusivity tensor (computed with equation (143) ) is smaller than the given threshold.

Alternatively, the parameter Number of Random Walks determines the number of molecules that are traced. The higher the number, the higher is the achieved accuracy. Convergence of the result for is not checked in this case and no given tolerance is achieved. This stopping criterion is only selectable if Fixed Distance was chosen as Travel Distance Mode.

Random Seed sets the seed of the underlying random number generator. The same random seed generates identical results; results with different random seeds should be similar but not the same. If results computed with different random seeds are significantly different, the Number of Random Walks and probably the Average Travel Distance values should be increased.

By checking Save Trajectory File, the particle trajectories are saved and can be visualized from the result viewer. It is not recommended to store the trajectories when the option Auto Distance, Check Convergence was chosen. In that case, the number of particles and the length of the trajectories typically becomes too large and the solver will fail due to a lack of RAM or hard disk space available.

Depending on the purchased license, the simulation process can be parallelized.

The Parallelization Options dialog box opens when clicking the Edit... button, to choose between Sequential, Parallel (Shared Memory) and Automatic Number Of Threads. When Parallel is chosen, the Number of Threads to run can be entered. If the entered number is larger than the one the license supports, an error message appears. For details on how to set up und run parallel computations, consult the High Performance Computations chapter.

Parallelization Benchmarks Result As an example for the parallelization, Knudsen diffusion in a microporous layer (MPL) is computed with different number of processes. The computation is run on a server with 2 x Intel E5-2697A v4 processors with 16 cores each, running with a maximum of 3.60 GHz, and 128 GB RAM. The MPL structure of size 2,000 x 2,000 x 2,000 was created with GrainGeo and ProcessGeo. It has a porosity of 64% The computation for the structure with 8 billion voxels requires only 32 GB of RAM. The effective Knudsen diffusivity for oxygen at 20°C in z-direction is 8.82e-05 m²/s. Runtimes for different number of parallel processes are shown in the following graph: