Discrete particle methods

Figure 7. Discrete particle methods for simulation of fluids. LB (lattice Boltzmann),...

Within the FPM, we can extend further the capabilities of the discrete particle method to the mesoscopic regime and show that they are competitive to standard simulation techniques with continuum equations. These methods establish a foundation for cross-scale computations ranging from nanoscales to microns and can provide a framework for studying the interaction of microstructures and large-scale flow, which may be of value in blood flow and other applications in polymeric flows (Banfield et al. 2000 Schwertman et al 1999 Hiemstra and VanReimsdijk 1999). 

Xu, B.H. and Yu, A.B. (1997), Numerical simulation of gas solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics, Chem. Eng. Sci., 52, 2785. 

There are two main approaches for the numerical simulation of the gas-solid flow 1) Eulerian framework for the gas phase and Lagrangian framework for the dispersed phase (E-L) and 2) Eulerian framework for all phases (E-E). In the E-L approach, trajectories of dispersed phase particles are calculated by solving Newton s second law of motion for each dispersed particle, and the motion of the continuous phase (gas phase) is modeled using an Eulerian framework with the coupling of the particle-gas interaction force. This approach is also referred to as the distinct element method or discrete particle method when applied to a granular system. The fluid forces acting upon particles would include the drag force, lift force, virtual mass force, and Basset history force.Moreover, particle-wall and particle-particle collision models (such as hard sphere model, soft sphere model, or Monte Carlo techniques) are commonly employed for this approach. In the E-E approach, the particle cloud is treated as a continuum. Local mean... 

Keywords Atomization Chemical reactions Craiservation equations Constitutive equations Drop breakup Drop deformation Drop collisions Evaporation LES Newtonian fluids RANS Spray modeling Spray PDF Stochastic discrete particle method Source terms Turbulence... 

The discretization of the liquid phase is achieved by the discrete particle method (c.f. Ref. [4]). In this method, the domain, X, of the spray PDF,/(t, X), is subdivided into hyper-rectangles, and all droplets that fall within one particular hyper-rectangle are identified as one representative particle. In other words, the spray PDF/(t, X) is approximated with a discrete PDF, where each discretization point corresponds to a representative particle consisting of droplets of identical states. The evolution of the spray PDF is then determined in analogy to the Monte Carlo method by using a sampling process on these particles. 

Modeling Mesoscopic Fluids with Discrete-Particles — Methods, Algorithms, and Results... 

FIGURE 26.3 Methodological framework for discrete particle methods with a listing of the spatial scales capable to be captured today and number of particles simulated on reasonably large shared-memory computer systems [22],... 

The computational problems involving multi-million particle ensembles, found in modeling mesoscopic phenomena, were considered only recently as the typical problems. Rapid increase of computational power of modem processors and growing popularity of coarse-grained discrete particle methods, such as dissipative particle dynamics, fluid particle model, smoothed particle hydrodynamics and LEG, allow for the modehng of complex problems by using smaller shared-memory systems [101]. 

The discrete-particle methods proposed earher can be used as the components of the problemsolving environment (PSE) based on the conception of multiresolutional wavelets. As shown in Figme 26.38, the whole series of simulations can be performed over three different spatio-temporal levels similarly as it is for wavelets but here the various shapes of wavelets will depend on the model of particle (atom, DPD droplet, FPM drop, and SPH chunk of fluid) and consequently the interactions between particles. In fact, the shapes of short-ranged interaction can be treated as some sort of wavelets. The interactions are short-ranged with compact support and well localized... 

In recent years, new discrete-particle methods have been developed for modeling physical and chemical phenomena occurring in the mesoscale. The most popular are grid-type techniques such as cellular automata (CA), LG, LBG, diffusion- and reaction-limited aggregation [37] and stochastic gridless methods, e.g., DSMC used for modeling systems characterized by a large Knudsen number [41], and SRD [39]. Unlike DSMC, in SRD collisions are modeled by simultaneous stochastic rotation of the relative velocities of every particle in each cell. 

Gridless discrete-particle methods have a few significant advantages over grid techniques. These advantages can be enumerated as follows ... 

On the other hand, the LBG method can capture both mesoscopic and macroscopic scales even larger than those that can be modeled by discrete-particle methods. This advantage is due to computational simplicity of the method, which comes from coarse-grained discretization of both the space and time and drastic simplification of collision rules between particles. We can look at the validity of these simplifications by comparing them with more realistic discrete-particles simulation. We regard both DPD and LBG as being complementary computational tools for modeling the slow dynamics in porous media over wide spatio-temporal scales. 

To analyze the individual heat transfer kinetics of droplet clusters within the spray of twin-fluid atomizers, the local correlations between the droplet concentration and the heat and flow conditions are evaluated. Numerical simulations of the spray flow analyzed in this paper have been carried out with Large-Eddy-Simulation (LES) models with Lagrangian particle tracking (discrete particle method) for the droplet motion. A synthetic perturbation generator [30] for the inflow conditions for the gas flow and simple perturbations are added to the dispersed phase to induce realistic vortex patterns at the nozzle and in the consequent spray. 

Thornton, A., Weinhart, T., Luding, S., and Bokhove, O. (2012). Modeling of particle size segregation Calibration using the discrete particle method. Int. J. Mod. Phys. C, 23(8). 

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