PathFinder (C) Wojciech Sobieski  a program destined for analysis the spatial structure of granular beds, or its parts, of a cylindrical or cubical shape (Fig. 1). The program is available free of charge with source code and can be used on Windows or Unix/Linux. The program needs additional software to work: gfortran compiler (for compiling source code), the Gnuplot environment (for basic visualization and analysis of the calculations) and ParaView (for the visualization and analysis of results). These programs are also available free of charge under the GPL license for both Windows and Unix/Linux.
Fig. 1 Examples of visualization of the results of calculations performed with the use of PathFinder program
Path Tracking Method (PTM) (C) Wojciech Sobieski  iterative method of determination of the length of pore channel in the chosen space direction, which consists in analyzing the local structure of the pore space based on vector geometry.
In the case of Pathfinder code, the length of pore channel is determined between two parallel planes based on the sum of the unitary lengths, calculated based on socalled tetrahedral structures (Fig. 2), which establish the basis for the calculation algorithm. Tetrahedral structures are created based on the data on the location and diameter of each particle in the bed. The data for calculations are obtained from DEM simulation or from the analysis of a set of tomography scans. Details concerning method are available in the User's Guide.
Fig. 2 Schema of the tetrahedral structure
Wojciech Sobieski developed PTM for granular beds in 2009 during an internship at the University of Manitoba in Winnipeg (see the official confirmation). The inspiration to start work on a method was observation, resulting from the author's extensive experience in programming, that DEM simulation results can be used to analyze the internal structure of porous media, in particular for the calculation of various geometrical parameters, including tortuosity. In 2009, the first working version of the program was created; the process of its creation was described in the Research Report 1/2009 (in Polish or in English) This report later became the basis for several articles in peerreviewed journals.
Licence: The conditions for using each of elements of the PathFinder project are as follows:
 The software is free of charge and can be used for any purpose by institutions and individuals.
 In case of publishing any material, for creation of which contributed the elements of the PathFinder project, in particular scientific articles, their authors are required to cite suitable articles from publication lists placed on the project website.
 In case of redistribution of the software, no part of the installation package can be removed, in particular the terms of the license.
 Copyright holders of each component of the project are indicated in the headers of the source code or in the documentation.
 The authors of the project are not responsible for any damage or losses resulting from the use of software and the use of the information contained therein. The authors also assure that they have made every effort to make the project errorfree and containing reliable information.
Features of PathFinder program:
 calculation of bed height (with a correction of its upper surface)
 calculation of bed volume
 calculation of pore volume of the bed
 calculation of porosity
 calculation of total outer surface of bed particles
 calculation of the specific surface area as defined by Kozeny and Carman
 determination of default starting coordinates for the socalled ninepoint method
 calculation of path length (a path that fluid will travel between particles, moving in flow direction  the Zaxis), in the five characteristic locations of bed
 calculation of path length using smoothing algorithm (for fluid can not change the direction of movement suddenly), in five characteristic locations of bed
 calculation of number of points and sections of path
 calculation of angles between successive segments of path and average angle
 computing total area and wet area for each triangle
 computing total perimeter, wet perimeter and friction perimeter for each triangle
 calculation of tortuosity
 calculation of tortuosity using the YuLi formula
 calculation of the linear term of KozenyCarman equation (with a model constant equal to 1)
 calculation of the linear and nonlinear terms of Ergun equation
 calculation of the deviation (distance) of path points from the plumbline
 visualization of the deviation (distance) of path points from the plumbline
 visualization of the spatial step changes in path points on Z directions
 visualization of the tortuosity distribution in characteristic bed points
Installation package contains also User's Guide as well as a few supporting tools:
 pathGUI  graphical interface (currently for Windows only)
 program converting PFC3D output files to PathFinder input files
 program converting YADE output files to PathFinder input files
 program calculating values of KozenyCarman equation for air flow
 program calculating values of Ergun equation for air flow
 program for sensitivity analysis of KozenyCarman and Ergun models
References:
 Sobieski W., Lipiński S.: The influence of particle size distribution on parameters characterizing the spatial structure of porous beds. GRANULAR MATTER, Vol. 21:14 (2019), 15 p. DOI: https://doi.org/10.1007/s100350190866x
 Sobieski W., Matyka M., Gołembiewski J., Lipiński S.: The Path Tracking Method as an alternative for tortuosity determination in granular beds. GRANULAR MATTER, Vol. 20:72 (2018), 14 p. DOI: https://doi.org/10.1007/s100350180842x
 Sobieski W., Lipiński S., Dudda W., Trykozko A., Marek M., Wiącek J., Matyka M., Gołembiewski J.:
Granular porous media (in Polish).
Department of Mechanics and Machine Design, Olsztyn 2016. ISBN 9788360493045.
 Dudda W., Sobieski W.:
Modification of the PathFinder algorithm for calculating granular beds with various particle size distributions.
TECHNICAL SCIENCES, Vol. 17, No 2 (2014), pp. 135148. ISSN 15054675.
 Sobieski W., Lipiński S.:
PathFinder User's Guide.
University of Warmia and Mazury in Olsztyn (Poland), 2013.
 Sobieski W., Zhang Q., Liu, C.:
Predicting tortuosity for airflow through porous beds consisting of randomly packed spherical particles.
TRANSPORT IN POROUS MEDIA, Vol. 93, No. 3 (2012), pp. 431451.
 Liu, C. Zhang Q., Chen Y.:
Discrete element simulations of vibration characteristics of bulk grain in storage bins.
Transactions of the ASABE, Vol. 53, No. 5 (2010), pp. 16531659.
 Sobieski W.:
Calculating tortuosity in a porous bed composed of spherical particles with known size and distribution in space. Research Report 1/2009.
 Sobieski W.:
GNU Fortran with data visualization elements (in Polish).
University of Warmia and Mazury, Olsztyn 2008, 403 pages.
 Liu, C., Zhang Q., Chen Y.:
PFC3D simulations of lateral pressures in model bins.
Paper No 083340 (2008). American Society of Agricultural and Biological Engineers, St. Joseph, MI. 13 pp.
 Liu, C., Zhang Q., Chen Y.:
PFC3D simulations of vibration characteristics of bulk solids in storage bins.
Paper No 083339 (2008), American Society of Agricultural and Biological Engineers, St. Joseph, MI. 14 pp.
