An Introduction to Modeling and Simulation of Particulate Flows Part 1 ppt

... developed in Zohdi [ 212 ] and [ 217 ]. 11 05 book2007/5 /15 page 16 ✐✐✐✐✐✐✐✐ 16 Chapter 2. Modeling of particulate flowswhere vcm(t) is the mean velocity of the group of particles and δvi(t) ... book2007/5 /15 page 14 ✐✐✐✐✐✐✐✐ 14 Chapter 2. Modeling of particulate flowswhere 12 ij(t +δt 1 ,t + δt)def= 1 miEin(t +δt 1 ,t + δt) − 1 mjEjn(t +δt 1 ,t + δt) (2 .14 ) and ij(t, ... words,α1ijmiT2L−(β 1 +1) system 1 =α1ijmiT2L−(β 1 +1) system 2 (1. 62) and α2ijmiT2L−(β2 +1) system 1 =α2ijmiT2L−(β2 +1) system 2 (1. 63)must hold simultaneously...

... haveω∗n=−α 1 β 1 r−β 1 1 ∗+ α2β2r−β2 1 ∗m=−α 1 mβ 1 r−β 1 1 ∗+ α2mβ2r−β2 1 ∗, (4.34)where the “loading” isf∗(t) =−α 1 r−β 1 ∗+ α2r−β2∗− α 1 β 1 r−β 1 1 ∗+ ... [13 1], Zohdi [208],[209], and the extensive works of Farhat and coworkers (Piperno et al. [16 3], Farhat et al.[65], Lesoinne and Farhat [13 0], Farhat and Lesoinne [66], Piperno and Farhat [16 4], ... Park and Felippa [16 1], Zienkiewicz [206],Schrefler [17 3], Lewis et al. [13 3], Doltsinis [52], [53], Piperno [16 2], Lewis and Schrefler [13 2], Armero and Simo [7]–[9], Armero [10 ], Le Tallec and...

... 530Z02468 10 12 14 16 X0Y0Z02468 10 12 14 16 X0Y0Z02468 10 12 14 16 X0Y0Z02468 10 12 14 16 X0Y0Z02468 10 12 14 16 X0Y0Z02468 10 12 14 16 X0YFigure6.5. Top ... [209]).0.20.40.60.8 1 1.2 1. 4 1. 6 1. 80 2 4 6 8 10 12 14 16 18 20FITNESSGENERATION8 PARTICLES 16 PARTICLES32 PARTICLES64 PARTICLES 12 8 PARTICLES00.5 1 1.522.533.540 2 4 6 8 10 12 14 16 18 20AVERAGE ... instabilities can become a primary concern.0Z02468 10 12 14 16 X0Y0Z02468 10 12 14 16 X0Y0Z02468 10 12 14 16 X0Y0Z02468 10 12 14 16 X0Y0Z02468 10 12 14 16 X0Y0Z02468 10 12 14 16 X0YFigure...

... the time step size of tlim= 10 −2s and a starting time step size of 10 −3s.The tolerances of both fields (TOLr and TOLθ) for the fixed-point iterations were set to 10 −6 and the upper limit ... have37 10 0 010 0 01 wL +1, K 1 wL +1, K2wL +1, K3=wL 1 wL22wL3− wL 1 3−tawL +1, K 1 1tbwL +1, K 1 2(t)2cwL +1, K 1 3. ... Armero [10 ], Le Tallec and Mouro [13 1], Zohdi [208], [209], and theextensive works of Farhat and coworkers (Piperno et al. [16 3], Farhat et al. [65], Lesoinne and Farhat [13 0], Farhat and Lesoinne...

... σf)i,j,k,L≈σi +1, j,k,Lf 11 − σi 1, j,k,Lf 11 2x 1 +σi,j +1, k,Lf 12 − σi,j 1, k,Lf 12 2x2+σi,j,k +1, Lf 13 − σi,j,k 1, Lf 13 2x3e 1 +σi +1, j,k,Lf 21 − σi 1, j,k,Lf 21 2x 1 +σi,j +1, k,Lf ... vf)i,j,k,L +1, K 1 +tρf∇x· σf+ρfbfi,j,k,L +1, K 1 .(8 .18 )In an abstract setting, we haveAf 1 ρL +1, Kf,θL +1, K 1 f, vL +1, K 1 f= Ff 1 ρL +1, K 1 f,θL +1, K 1 f, vL +1, K 1 f, ... 2ρL +1, Kf,θL +1, Kf, vL +1, K 1 f= Ff 2ρL +1, Kf,θL +1, K 1 f, vL +1, K 1 f, (ENERGY),Af 3ρL +1, Kf,θL +1, Kf, vL +1, Kf= Ff 3ρL +1, Kf,θL +1, Kf, vL +1, K 1 f,...

... Forreviews of such systems, see Chokshi et al. [43], Dominik and Tielens [54], Mitchell and Frenklach [14 8], Charalampopoulos and Shu [39], [40], and Zohdi [ 212 ]–[ 219 ].9 .1. 1 Ray theory: Scope of useIn ... presence of near-fields causes particletrajectories due to mutual attraction and repulsion, and particles to make contact frequently.05 book2007/5 /15 page 10 1✐✐✐✐✐✐✐✐8.7. Summary 10 1Table ... error tolerance within a time step set to TOL 1 = TOL2= TOL3= TOL4= 10 −3.8.6 Discussion of the resultsFor this system, the Reynolds number, based on the mean particle diameter and initial...

... 10 −3kg/m3 1 0. 214 80 5.82056 0.53687 0 .15 078 0.04968 310 20. 214 81 5. 912 42 0.537 41 0 .15 152 0.0 512 64063 0. 214 82 5.8 912 1 0.53637 0 .15 152 0.0 516 6 210 40. 214 82 5.83350 0.53636 0 .15 150 0.052328775 0. 214 77 ... 12 9 518 .809504.222489.635475.048460.46445.8734 31. 286 416 .698402 .11 1387.524372.936358.349343.762329 .17 5 314 .587 518 .809504.222489.635475.048460.46445.8734 31. 286 416 .698402 .11 1387.524372.936358.349343.762329 .17 5 314 .587 518 .809504.222489.635475.048460.46445.8734 31. 286 416 .698402 .11 1387.524372.936358.349343.762329 .17 5 314 .587 518 .809504.222489.635475.048460.46445.8734 31. 286 416 .698402 .11 1387.524372.936358.349343.762329 .17 5 314 .587Figure9 .15 . Continuing Figure9 .14 , top to bottomand leftto ... 12 7 518 .809504.222489.635475.048460.46445.8734 31. 286 416 .698402 .11 1387.524372.936358.349343.762329 .17 5 314 .587 518 .809504.222489.635475.048460.46445.8734 31. 286 416 .698402 .11 1387.524372.936358.349343.762329 .17 5 314 .587 518 .809504.222489.635475.048460.46445.8734 31. 286 416 .698402 .11 1387.524372.936358.349343.762329 .17 5 314 .587 518 .809504.222489.635475.048460.46445.8734 31. 286 416 .698402 .11 1387.524372.936358.349343.762329 .17 5 314 .587Figure...

... [17 4], van der Wal and Becker [19 7], Chyu and Shah [46], and Libby [13 4], [13 5], Libby et al. [13 6], Libby and Aikawa [13 7], Richardson et al. [16 9], Loreeet al. [14 1], and Davies et al. [ 51] , ... Kaazempur-Mofrad et al. [11 5], Chauet al. [ 41] , Chan et al. [38], Dai et al. [49], Khalil et al. [12 1], Khalil et al. [12 2], Stroudet al. [18 0], [18 1], Berger and Jou [29], and Jou and Berger [11 2]. For experimentallyoriented ... Kahn and Hackett [11 7], [11 8], and Zohdi and Szeri [222].Clearly, the number of applications in the biological sciences is enormous and growing.More general information on the theory and simulations...

... Medicine, Vol. 8, 12 57 12 62. [13 8] Lissauer, J. J. 19 93. Planet formation.Annual Review of Astronomy and Astrophysics,Vol. 31, 12 9 17 4. [13 9] Liu, C. H., Jaeger, H. M., and Nagel, S. R. 19 91. Finite ... coupling.Journal of Fluid Mechanics, Vol. 429, 23– 61. [ 61] Duran, J. 19 97. Sands, Powders and Grains. An Introduction to the Physics of Gran-ular Matter. Springer-Verlag.[62] Eber, S. and Lux, S. ... Semiconductor Man-ufacturing, Vol. 14 , 11 2 13 3. [14 4] Luo, L. and Dornfeld, D. A. 2003. Effects of abrasive size distribution in chemical-mechanical planarization: Modeling and verification. IEEE Transactions:...