Outline of The Method
A DEM-simulation is started by first generating a model, which results in spatially orienting all particles and assigning an initial velocity. The forces which act on each particle are computed from the initial data and the relevant physical laws and contact models. Generally, a simulation consists of three parts: the initialization, explicit time-stepping, and post-processing. The time-stepping usually requires a nearest neighbor sorting step to reduce the number of possible contact pairs and decrease the computational requirements; this is often only performed periodically.
The following forces may have to be considered in macroscopic simulations:
- friction, when two particles touch each other;
- contact plasticity, or recoil, when two particles collide;
- gravity, the force of attraction between particles due to their mass, which is only relevant in astronomical simulations.
- attractive potentials, such as cohesion, adhesion, liquid bridging, electrostatic attraction. Note that, because of the overhead from determining nearest neighbor pairs, exact resolution of long-range, compared with particle size, forces can increase computational cost or require specialized algorithms to resolve these interactions.
On a molecular level, we may consider
- the Coulomb force, the electrostatic attraction or repulsion of particles carrying electric charge;
- Pauli repulsion, when two atoms approach each other closely;
- van der Waals force.
All these forces are added up to find the total force acting on each particle. An integration method is employed to compute the change in the position and the velocity of each particle during a certain time step from Newton's laws of motion. Then, the new positions are used to compute the forces during the next step, and this loop is repeated until the simulation ends.
Typical integration methods used in a discrete element method are:
- the Verlet algorithm,
- velocity Verlet,
- symplectic integrators,
- the leapfrog method.
Read more about this topic: Discrete Element Method
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