Сандық бөлшектер әдісі: Көптеген ұсақ бөлшектердің қозғалысын және әсерін есептеу

Numerical methods for computing the motion and effect of a large number of small particles

A discrete element method (DEM), also called a distinct element method, is any of a family of numerical methods for computing the motion and effect of a large number of small particles. Though DEM is very closely related to molecular dynamics, the method is generally distinguished by its inclusion of rotational degrees of freedom as well as stateful contact, particle deformation and often complicated geometries (including polyhedra). With advances in computing power and numerical algorithms for nearest neighbor sorting, it has become possible to numerically simulate millions of particles on a single processor. Today DEM is becoming widely accepted as an effective method of addressing engineering problems in granular and discontinuous materials, especially in granular flows, powder mechanics, ice and rock mechanics. DEM has been extended into the Extended Discrete Element Method taking heat transfer, chemical reaction and coupling to CFD and FEM into account. Discrete element methods are relatively computationally intensive, which limits either the length of a simulation or the number of particles. Several DEM codes, as do molecular dynamics codes, take advantage of parallel processing capabilities (shared or distributed systems) to scale up the number of particles or length of the simulation. An alternative to treating all particles separately is to average the physics across many particles and thereby treat the material as a continuum. In the case of solid like granular behavior as in soil mechanics, the continuum approach usually treats the material as elastic or elasto plastic and models it with the finite element method or a mesh free method. In the case of liquid like or gas like granular flow, the continuum approach may treat the material as a fluid and use computational fluid dynamics. Drawbacks to homogenization of the granular scale physics, however, are well documented and should be considered carefully before attempting to use a continuum approach.

The various branches of the DEM family are the distinct element method proposed by Peter A. Cundall and Otto D. L. Strack in 1979, the generalized discrete element method, the discontinuous deformation analysis (DDA) and the finite discrete element method concurrently developed by several groups (e. g., Munjiza and Owen). The general method was originally developed by Cundall in 1971 to problems in rock mechanics. Williams Bicanic, and Bobet et al. (see below). A comprehensive treatment of the combined Finite Element Discrete Element Method is contained in the book The Combined Finite Discrete Element Method.

The discrete element method is widely applied for the consideration of mechanical interactions in many body problems, particularly granular materials. Among the various extensions to DEM, the consideration of heat flow is particularly useful. Generally speaking in Thermal DEM methods, the thermo mechanical coupling is considered, whereby the thermal properties of an individual element are considered in order to model heat flow through a macroscopic granular or multi element medium subject to a mechanical loading. Interparticle forces, computed as a part of classical DEM, are used to determined areas of true interparticle contact and thus model the conductive transfer of heat from one solid element to another. A further aspect that is considered in DEM is the gas phase conduction, radiation and convection of heat in the interparticle spaces. To facilitate this, properties of the inter element gaseous phase need to be considered in terms of pressure, gas conductivity and the mean free path of gas molecules.

Following the work by Munjiza and Owen, the combined finite discrete element method has been further developed to various irregular and deformable particles in many applications including pharmaceutical tableting, packaging and flow simulations, and impact analysis.