Discrete particle models

The methods used for modeling pure granular flow are essentially borrowed from that of a molecular gas. Similarly, there are two main types of models the continuous (Eulerian) models (Dufty, 2000) and discrete particle (Lagrangian) models (Herrmann and Luding, 1998 Luding, 1998 Walton, 2004). The continuum models are developed for large-scale simulations, where the controlling equations resemble the Navier-Stokes equations for an ordinary gas flow. The discrete particle models (DPMs) are typically used in small-scale simulations or... 

DPMs offer a viable tool to study the macroscopic behavior of assemblies of particles and originate from MD methods. Initiated in the 1950s by Alder and Wainwright (1957), MD is by now a well-developed method with thousands of papers published in the open literature on just the technical and numerical aspects. A thorough discussion of MD techniques can be found in the book by Allen and Tildesley (1990), where the details of both numerical algorithms and computational tricks are presented. Also, Frenkel and Smit (1996) provide a comprehensive introduction to the recipes of classical MD with emphasis on the physics underlying these methods. Nearly all techniques developed for MD can be directly applied to discrete particles models, except the formulation of particle-particle interactions. Based on the mechanism of particle-particle interaction, a granular system may be modeled either as hard-spheres or as soft-spheres. ... 

Bokkers, G. A., Van Sint Annaland, M., and Kuipers, J. A. M., Comparison of continuum models using kinetic theory of granular flow with discrete particle models and experiments extent of particle mixing induced by bubbles. Proceedings of Fluidization XI, May 9-14, 2004, 187-194, Naples, Italy (2004). 

Consider an example from nucleation and growth of thin films. At least three length scales can be identified, namely, (a) the fluid phase where the continuum approximation is often valid (that may not be the case in micro- and nanodevices), (b) the intermediate scale of the fluid/film interface where a discrete, particle model may be needed, and (c) the atomistic/QM scale of relevance to surface processes. Surface processes may include adsorption, desorption, surface reaction, and surface diffusion. Aside from the disparity of length scales, the time scales of various processes differ dramatically, ranging from picosecond chemistry to seconds or hours for slow growth processes (Raimondeau and Vlachos, 2002a, b). 

Fig. 7. Schematic illustrating the coupling of a fluid-phase mass transfer model with a discrete, particle model, such as KMC, through the boundary condition. The continuum model passes the external field and the KMC simulation computes spatial and temporal rates that are needed in the boundary condition of the continuum model.

Similar to the role that DNS and discrete particle models (see Section IV,B,3) might play in the development of improved turbulence models, which can be used in engineering applications, and closure laws for gas-solid continuum models. Brownian dynamics (BD) should be mentioned as a powerful tool to develop closure models for non-Newtonian fluids (Brady and Bossis, 1988). 

Development of improved closure laws for the rheological description of fluidized suspensions on basis of discrete particle models... 

Trapp, J. A., and Mortensen, G. A., A discrete particle model for bubble slug two-phase flow. J. Comp. Phys. 107, 367 (1993). 

Discrete particle models/ Eillerian-Lagi angian models... 

At a higher level, the flow field is modeled at a scale much larger than the size of the particles, and the fluid velocity and pressure are obtained by solving the volume-averaged Navier-Stokes equations. The particle particle interactions (particle wall as well) are formulated with the so-called discrete particle models (DPMs), which are based on the schemes that are traditionally used in molecular dynamics simulations, with the addition of dissipation of mechanical energy. 

J. M. Link, C. Zeilstra, N. G. Deen and J. A. M. Kuipers, Validation of a discrete particle model in a 2D spout-fluid bed using non-intrusive optical measuring techniques, Can. J. Chem. Eng., 2004, 82, 30. 

Similar schemes of coarse-graining can be realized by using off-grid discrete-particles models. In the following sections, some competitive ideas to LEG approach will be presented. 

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