Discrete-particles, algorithmic methods

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. ... 

Using advances in computer reconstruction methods (see e.g. Kikkinides and Burganos, 2000 Torquato, 2001) and past experience with discrete particle deposit simulations (Konstandopoulos, 2000), we have developed algorithmic as well as process-based reconstruction techniques to generate three-dimensional (3D) digital materials that are faithful representations of DPF microstructures. We refer to this approach as DPF microflow simulation (MicroFlowS). MicroFlowS is thus a short name for a computational approach, which combines... 

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

I. M. Yassin, N. M. Tahir, M. K. M. Salleh, H. A. Hassan, A. Zabidi, and H. Z. Abidin, "Novel Mutative Particle Swarm Optimization Algorithm for Discrete Optimization in The 2009 International Conference on Genetic and Evolutionary Methods (GEM09), Las Vegas, NV,2009,pp. 137-142. 

Though this new algorithm still requires some time step refinement for computations with highly inelastic particles, it turns out that most computations can be carried out with acceptable time steps of 10 5 s or larger. An alternative numerical method that is also based on the compressibility of the dispersed particulate phase is presented by Laux (1998). In this so-called compressible disperse-phase method the shear stresses in the momentum equations are implicitly taken into account, which further enhances the stability of the code in the quasi-static state near minimum fluidization, especially when frictional shear is taken into account. In theory, the stability of the numerical solution method can be further enhanced by fully implicit discretization and simultaneous solution of all governing equations. This latter is however not expected to result in faster solution of the TFM equations since the numerical efforts per time step increase. 

The pneumatic drying model was solved numerically for the drying processes of sand particles. The numerical procedure includes discretization of the calculation domain into torus-shaped final volumes, and solving the model equations by implementation of the semi-implicit method for pressure-linked equations (SIMPLE) algorithm [16]. The numerical procedure also implemented the Interphase Slip Algorithm (IPSA) of [17] in order to account the various coupling between the phases. The simulation stopped when the moisture content of a particle falls to a predefined value or when the flow reaches the exit of the pneumatic dryer. 

In this approach, the finite volume methods discussed in the previous chapter can be applied to simulate the continuous fluid (in a Eulerian framework). Various algorithms for treating pressure-velocity coupling, and the discussion on other numerical issues like discretization schemes are applicable. The usual interpolation practices (discussed in the previous chapter) can be used. When solving equations of motion for a continuous fluid in the presence of the dispersed phase, the major differences will be (1) consideration of phase volume fraction in calculation of convective and diffusive terms, and (2) calculation of additional source terms due to the presence of dispersed phase particles. For the calculation of phase volume fraction and additional source terms due to dispersed phase particles, it is necessary to calculate trajectories of the dispersed phase particles, in addition to solving the equations of motion of the continuous phase. 

Abstract. In the present paper the problem of reuse water networks (RWN) have been modeled and optimized by the application of a modified Particle Swarm Optimization (PSO) algorithm. A proposed modified PSO method lead with both discrete and continuous variables in Mixed Integer Non-Linear Programming (MINLP) formulation that represent the water allocation problems. Pinch Analysis concepts are used jointly with the improved PSO method. Two literature problems considering mono and multicomponent problems were solved with the developed systematic and results has shown excellent performance in the optimality of reuse water network synthesis based on the criterion of minimization of annual total cost. 

Method for optimization of the maintenance activities in the nuclear power plant is presented. The optimization is done with the apphcation of the modified particle swarm optimization algorithm. The safety of the system is assessed throng the mean value of the system unavailabihty calculated for discrete time points. 

The integration of deterministic particle trajectories is not problematic since it is possible to draw from the vast body of known algorithms for ODEs. However, whereas exact deterministic trajectories must always remain within the integration domain (except at open boundaries), the discretized versions obtained by any numerical scheme will be subjected to a finite discretization error. This error has two main consequences with far-reaching computational effects in micro/macro methods. 

The closed equation (12.383) does not necessary conserve the moments of the distribution due to the macroscopic or finite grid resolution employed in the size domain, thus some sort of ad hoc numerical correction must be induced to enforce the conservative moment properties. It is noted that it is mainly at this point in the formulation of the numerical algorithms that the class method of Hounslow et al. [88], the discrete fixed pivot method of Kumar and Ramkrishna [112] and the multi-group approach used by Carrica et al. [30], among others, differs to some extent. The problem in question is related to the birth terms only. Following the discrete fixed pivot method of Kumar and Ramkrishna [112], the formation of a particle of size in size range... 

The discrete pivot method provides information on the particle size distribution that is needed in the multi-fluid framework and can also be used for proper validation of the source term closures. However, in order to cover a broad range in the particle size distribution, a large number of sections are often needed making these algorithms rather time consuming. To ensure mass conservation, the smallest particles are generally not allowed to break and the largest particles are normally not involved in the coalescence process. 

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