By T.I. Zohdi
The rather fresh bring up in computational strength to be had for mathematical modeling and simulation increases the chance that sleek numerical tools can play an important function within the research of complicated particulate flows. This introductory monograph specializes in simple types and bodily established computational answer innovations for the direct and quick simulation of flowing particulate media. Its emphasis is totally on fluidized dry particulate flows during which there is not any major interstitial fluid, even though totally coupled fluid-particle structures are mentioned besides. An advent to uncomplicated computational tools for ascertaining optical responses of particulate platforms is also incorporated. The profitable research of quite a lot of functions calls for the simulation of flowing particulate media that concurrently comprises near-field interplay and speak to among debris in a thermally delicate atmosphere. those structures obviously take place in astrophysics and geophysics; powder processing pharmaceutical industries; bio-, micro- and nanotechnologies; and purposes bobbing up from the learn of spray tactics related to aerosols, sputtering, and epitaxy. viewers An creation to Modeling and Simulation of Particulate Flows is written for computational scientists, numerical analysts, and utilized mathematicians and should be of curiosity to civil and mechanical engineers and fabrics scientists. it's also appropriate for first-year graduate scholars within the technologies, engineering, and utilized arithmetic who've an curiosity within the computational research of advanced particulate flows. Contents record of Figures; Preface; bankruptcy 1: basics; bankruptcy 2: Modeling of particulate flows; bankruptcy three: Iterative answer schemes; bankruptcy four: consultant numerical simulations; bankruptcy five: Inverse problems/parameter identity; bankruptcy 6: Extensions to swarm-like platforms; bankruptcy 7: complex particulate move types; bankruptcy eight: Coupled particle/fluid interplay; bankruptcy nine: uncomplicated optical scattering equipment in particulate media; bankruptcy 10: remaining comments; Appendix A. uncomplicated (continuum) fluid mechanics; Appendix B. Scattering; Bibliography; Index
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Additional info for An introduction to modeling and simulation of particulate flows
2) in the absence of near-field interaction. 22) thus indicating the rather obvious fact that energy is lost with each subsequent impact for e < 1. Now consider a group of flowing particles, each with different velocity. 24) ✐ ✐ ✐ ✐ ✐ ✐ ✐ 16 05 book 2007/5/15 page 16 ✐ Chapter 2. Modeling of particulate ﬂows where v cm (t) is the mean velocity of the group of particles and δv i (t) is a purely fluctuating (about the mean) part of the velocity. For the entire group of particles at time = t, Np Np mi (v cm (t) + δv i (t)) · (v cm (t) + δv i (t)) mi v i (t) · v i (t) = i=1 i=1 Np = Mv cm (t) · v cm (t) + 2v cm (t) · Np mi δv i (t) + i=1 mi δv i (t) · δv i (t).
In the upcoming algorithm, inbreeding is mitigated, since, with each new generation, new parameter sets, selected at random within the parameter space, are added to the population. 1. A typical cost function. ✐ ✐ ✐ ✐ ✐ ✐ ✐ 42 05 book 2007/5/15 page 42 ✐ Chapter 5. Inverse problems/parameter identiﬁcation superior parents. Additionally, parent retention is computationally less expensive, since these parameter sets do not have to be reevaluated (or ranked) in the next generation. An implementation of such ideas is as follows (Zohdi –).
2. The best parameter set’s (α 1 , α 2 , β1 , β2 ) objective function value with passing generations (Zohdi ). 3. Simulation results using the best parameter set’s (α 1 , α 2 , β1 , β2 ) values (for one random realization (Zohdi )). Remark. The specific structure of the interaction forces chosen was only one of many possibilities to model near-field flow behavior, for example, from the field of molecular dynamics (MD). The term “molecular dynamics” refers to mathematical models of systems of atoms or molecules where each atom (or molecule) is represented by a material point in R 3 and is treated as a point mass.