Drag Force Calculations in Polydisperse DEM Simulations with the Coarse-Grid Method: Influence of the Weighting Method and Improved Predictions Through Artificial Neural Networks

  • Pouyan PirniaEmail author
  • François Duhaime
  • Yannic Ethier
  • Jean-Sébastien Dubé


Several methods are employed for drag force calculations with the discrete element method depending on the desired accuracy and the number of particles involved. For many applications, the fluid motion cannot be solved at the pore scale due to the heavy computational cost. Instead, the coarse-grid method (CGM) is often used. It involves solving an averaged form of the Navier–Stokes equations at the continuum scale and distributing the total drag force among the particles. For monodisperse assemblages, the total drag force can be uniformly distributed among the particles. For polydisperse assemblages, however, the total CGM drag force must be weighted. It can be applied proportionally to the volume (CGM-V) or surface (CGM-S) of each particle. This article compares the CGM-V and CGM-S weighting methods with the weighting obtained by solving the Navier–Stokes equations at the pore scale with the finite element method (FEM). Three unit cells (simple cubic, body-centered cubic and face-centered cubic) corresponding to different porosity values, (respectively, 0.477, 0.319 and 0.259) were simulated. Each unit cell involved a skeleton of large particles and a smaller particle with variable size and position. It was found that both the CGM-V and CGM-S weighting methods do not generally give accurate drag force values for the smaller particles in a polydisperse assemblage, especially for large-size ratios. An artificial neural network (ANN) was trained using the FEM drag force as the target data to predict the drag force on smaller particles in a granular skeleton. The trained ANN showed a very good agreement with the FEM results, thus presenting ANN as a possible avenue to improve drag force weighting for the coarse-grid method.


Drag force Coarse-grid method Discrete elements Finite elements Artificial neural network 



The authors gratefully acknowledge the support of Hydro-Québec and NSERC for this project, and the helpful comments of one reviewer.

Author Contributions

PP developed the theory, calculated the drag forces and created the artificial neural network. He wrote the paper. FD developed the theory and supervised the project. He also revised and improved the manuscript. YE reviewed and edited the manuscript. JSD reviewed and edited the manuscript.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Laboratory for Geotechnical and Geoenvironmental Engineering (LG2)École de technologie supérieureMontrealCanada

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