DEM Simulations of Settling of Spherical Particles using a Soft Contact Model and Adaptive Time Stepping
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Published
Sep 21, 2024
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Abstract
We present a simple and flexible Discrete Element Method (DEM) model for simulating the dynamics of spherical particle systems. The aim is to utilize commonly available ODE integrators that are usually inappropriate for DEM, in particular the Runge-Kutta-Merson and Dormand-Prince solvers with adaptive time stepping. This is achieved by using a novel soft contact model with repulsive and frictional forces smoothly varying in time, which allows the time step adaptivity algorithms to work properly. The model parameters are calibrated so that a realistic random close packing can be obtained from simulations of particle settling at the bottom of a container. A reference minimal implementation in MATLAB and a complete implementation in C with OpenMP parallelization are introduced and their computational performance is assessed.
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Strachota, P.
(2024).
DEM Simulations of Settling of Spherical Particles using a Soft Contact Model and Adaptive Time Stepping.
Proceedings Of The Conference Algoritmy, , 225 -234.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/2176/1044
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References
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[18] P. Strachota and M. Beneš. A hybrid parallel numerical algorithm for three-dimensional phase field modeling of crystal growth. In A. Handlovičová and D. Ševčovič, editors, ALGORITMY 2016, 20th Conference on Scientific Computing, Vysoké Tatry - Podbanské, Slovakia, March 14 - 18, 2016. Proceedings of contributed papers, pages 23–32. Comenius University, Bratislava, 2016.
[19] P. Strachota, A. Wodecki, and M. Beneš. Focusing the latent heat release in 3D phase field simulations of dendritic crystal growth. Modelling Simul. Mater. Sci. Eng., 29:065009, 2021.
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method for dense particulate flows. International Journal of Multiphase Flow,
22(2):379–402, 1996.
[2] M. Beneš, P. Eichler, J. Hrdlička, J. Klinkovský, M. Kolář, T. Smejkal, P. Skopec, J. Solovský, P. Strachota, and A. Žák. Experimental validation of multiphase particle-in-cell simulations of fluidization in a bubbling fluidized bed combustor. Powder Technol., 416:118204, 2023.
[3] M. A. Benmebarek and M. M. Rad. Effect of rolling resistance model parameters on 3D DEM modeling of coarse sand direct shear test. Materials, 16:2077, 2023.
[4] N. Berry, Y. Zhang, and S. Haeri. Contact models for the multi-sphere discrete element method. Powder Technol., 416:118209, 2023.
[5] J. C. Butcher. Numerical Methods for Ordinary Differential Equations. Wiley, Chichester, 2nd edition, 2008.
[6] U. Caliskan and S. Miskovic. A chimera approach for MP-PIC simulations of dense particulate flow using large parcel size relative to the computational cell size. Chemical Engineering Journal Advances, 5:100054, 2020.
[7] J. Christiansen. Numerical solution of ordinary simultaneous differential equations of the 1st order using a method for automatic step change. Numer. Math., 14:317–324, 1970.
[8] L. Dagum and R. Menon. Openmp: An industry standard API for shared-memory programming. Computational Science & Engineering, IEEE, 5(1):46–55, 1998.
[9] A. Di Renzo and F. P. Di Maio. Comparison of contact-force models for the simulation of collisions in DEM-based granular flow codes. Chemical Engineering Science, 59:525–541, 2004.
[10] H. Kruggel-Emden, M. Sturm, S. Wirtz, and V. Scherer. Selection of an appropriate time integration scheme for the discrete element method (DEM). Comput. Chem. Eng., 32:2263–2279, 2008.
[11] G. Kuwabara and K. Kono. Restitution coefficient in a collision between two spheres. Jpn. J. Appl. Phys., 26(8):1230–1233, 1987.
[12] H.-G. Matuttis and J. Chen. Understanding the Discrete Element Method: Simulation of Non-Spherical Particles for Granular and Multi-body Systems. Wiley, 2014.
[13] P. J. O’Rourke and D. M. Snider. Inclusion of collisional return-to-isotropy in the MP-PIC method. Chemical Engineering Science, 80:39–54, 2012.
[14] P. J. O’Rourke and D. M. Snider. An improved collision damping time for MP-PIC calculations of dense particle flows with applications to polydisperse sedimenting beds and colliding particle jets. Chemical Engineering Science, 65(22):6014–6028, 2010.
[15] J. Rojek. Contact Modeling for Solids and Particles, chapter Contact Modeling in the Discrete Element Method, pages 177–228. Springer, 2018.
[16] H. Sigurgeirsson, A. Stuart, and W.-L. Wan. Algorithms for particle-field simulations with collisions. J. Comput. Phys., 172:766–807, 2001.
[17] P. Strachota. Three-dimensional numerical simulation of water freezing and thawing in a container filled with glass beads. arXiv, (arXiv:2401.01672):1–12, 2024.
[18] P. Strachota and M. Beneš. A hybrid parallel numerical algorithm for three-dimensional phase field modeling of crystal growth. In A. Handlovičová and D. Ševčovič, editors, ALGORITMY 2016, 20th Conference on Scientific Computing, Vysoké Tatry - Podbanské, Slovakia, March 14 - 18, 2016. Proceedings of contributed papers, pages 23–32. Comenius University, Bratislava, 2016.
[19] P. Strachota, A. Wodecki, and M. Beneš. Focusing the latent heat release in 3D phase field simulations of dendritic crystal growth. Modelling Simul. Mater. Sci. Eng., 29:065009, 2021.
[20] C. Thornton. Granular Dynamics, Contact Mechanics and Particle System Simulations: A DEM study. Sprin, 2015.
[21] S. Torquato, T. M. Truskett, and P. G. Debenedetti. Is random close packing of spheres well defined? Phys. Rev. Lett., 84(10):2064–2067, March 2000.
[22] V. Verma and J. T. Padding. A novel approach to MP-PIC: Continuum particle model for dense particle flows in fluidized beds. Chem. Eng. Sci.: X, 6:100053:1–13, 2020.
[23] O. R. Walton and R. L. Braun. Viscosity, granular-temperature, and stress calculations for shearing assemblies of inelastic, frictional disks. J. Rheol., 30:949–980, 1986.
[24] A. Žák, M. Beneš, and T. H. Illangasekare. Pore-scale model of freezing inception in a porous medium. Comput. Methods Appl. Mech. Eng., 414:116166, 2023.