Editing Discrete element method (section)

==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 (chemistry)|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 exclusion principle|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 [[numerical ordinary differential equations|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 [[program loop|loop]] is repeated until the simulation ends.

Typical integration methods used in a discrete element method are:
* the [[Verlet integration|Verlet algorithm]],
* [[velocity Verlet]],
* [[symplectic integrator]]s,
* the [[leapfrog method]].