Modeling Complex Multiphysics Systems with Discrete Element Method Enriched with the Kernel-Independent Fast Multipole Method

TL;DR

This work addresses the challenge of incorporating long-range interactions into discrete element method (DEM) simulations by coupling MercuryDPM with a kernel-independent fast multipole method (KIFMM). The approach uses rigid clumps to represent complex, non-spherical particles with distributed charges, enabling efficient and scalable simulations of electrostatic, dipole-dipole, and gravitational interactions across multiple scales. Four application examples demonstrate the framework’s versatility and performance, highlighting its potential for multiscale, multiphysics particle systems. The authors also outline future directions, including coupling with boundary-integral equations and further scalability improvements, with the codebase publicly available for broader use.

Abstract

The paper describes the coupling of the MercuryDPM discrete element method (DEM) code and the implementation of the kernel-independent fast multipole method (KIFMM). The combined simulation framework allows addressing the large class of multiscale problems, including both the mechanical interactions of particulates at the fine scale and the long-range interactions of various natures at the coarse scale. Among these are electrostatic interactions in powders, clays, and particulates, magnetic interactions in ferromagnetic granulates, and gravitational interactions in asteroid clouds. The formalism of rigid clumps is successfully combined with KIFMM, enabling addressing problems involving complex long-large interactions between non-spherical particles with arbitrary charge distributions. The capabilities of our technique are demonstrated in several application examples.

Figures (4)

• Figure 1: Identical charged particles in the box. (A) Snapshots of the system evolution at the beginning of the simulation ($\hat{t} = 0$), after $2 \times 10^4$ timesteps ($\hat{t} = 0.05$), and after $10^5$ timesteps ($\hat{t} = 1$). (B) Time evolution of the potential energy of long-range interactions $U_{LR}$ during the simulation. (C) Final stable configuration of particles at one of the sides of the box.
• Figure 2: Aggregation of interacting dipoles. (A) Snapshots of the system at $\hat{t} = 0$, $\hat{t} = 0.05$, $\hat{t} = 1$. (B) Time evolution of the potential energy of long-range interactions $U_{LR}$ during the simulation. (C) Evolution of the gravitational potential energy $U_{gra}$, elastic potential energy $U_{ela}$ and kinetic energy $U_{kin}$ during the simulation.
• Figure 3: Stacking of dipole platelets. (A) Snapshots of the system at $\hat{t} = 0$, $\hat{t} = 0.05$, $\hat{t} = 0.15$, $\hat{t} = 1$. (B) Time evolution of the potential energy of long-range interactions $U_{LR}$ during the simulation. (C) Evolution of translational ($U_{tra}$), rotational($U_{rot}$) and total ($U_{kin}$) kinetic energy, and the energy of elastic deformations ($U_{ela}$) during the simulation.
• Figure 4: Gravitational collapse of elastic particles. (A) Snapshots of the system at $\hat{t} = 0$, $\hat{t} = 0.2$, $\hat{t} = 0.3$, $\hat{t} = 1$. (B) Time evolution of the potential energy of long-range interactions $U_{LR}$ during the simulation. (C) Evolution of the total kinetic energy ($U_{kin}$), and the energy of elastic deformations ($U_{ela}$) during the simulation.