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Computation of strongly coupled multifield interaction in particle-fluid systems. (English) Zbl 1173.76418

Summary: The present work develops a flexible and robust solution strategy to resolve coupled systems comprised of large numbers of flowing particles embedded within a fluid. A model problem, consisting of particles which may undergo inelastic collisions in the presence of near-field forces, is considered. The particles are surrounded by a continuous interstitial fluid which is assumed to obey the compressible Navier-Stokes equations. Thermal effects are also considered. Such particle/fluid systems are strongly coupled, due to the mechanical forces and heat transfer induced by the fluid onto the particles and vice-versa. Because the coupling of the various particle and fluid fields can dramatically change over the course of a flow process, a primary focus of this work is the development of a recursive “staggering” solution scheme, whereby the time-steps are adaptively adjusted to control the error associated with the incomplete resolution of the coupled interaction between the various solid particulate and continuum fluid fields. A central feature of the approach is the ability to account for the presence of particles within the fluid in a straightforward manner that can be easily incorporated within any standard computational fluid mechanics code based on finite difference, finite element or finite volume type discretization. A three dimensional example is provided to illustrate the overall approach.

MSC:

76T15 Dusty-gas two-phase flows
76M20 Finite difference methods applied to problems in fluid mechanics
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[1] Ahmed, A. M.; Elghobashi, S. E., Direct numerical simulation of particle dispersion in homogeneous turbulent shear flows, Phys. Fluids, 13, 3346-3364 (2001) · Zbl 1184.76021
[2] Ahmed, A. M.; Elghobashi, S. E., On the mechanisms of modifying the structure of turbulent homogeneous shear flows by dispersed particles, Phys. Fluids, 12, 2906-2930 (2000) · Zbl 1184.76020
[3] Ames, W. F., Numerical Methods for Partial Differential Equations (1977), Academic Press · Zbl 0219.35007
[4] J. Bale-Glickman, K. Selby, D. Saloner, O. Savas, Physiological flow studies in exact-replica atherosclerotic carotid bifurcation, in: Proceedings of IMECE’03,2003 ASME International Mechanical Engineering Congress and Exposition, Washington, DC, 2003, pp. 16-21.; J. Bale-Glickman, K. Selby, D. Saloner, O. Savas, Physiological flow studies in exact-replica atherosclerotic carotid bifurcation, in: Proceedings of IMECE’03,2003 ASME International Mechanical Engineering Congress and Exposition, Washington, DC, 2003, pp. 16-21.
[5] Bale-Glickman, J.; Selby, K.; Saloner, D.; Savas, O., Experimental flow studies in exact-replica phantoms of atherosclerotic carotid bifurcations under steady input conditions, J. Biomech. Engrg., 125, 38-48 (2003)
[6] Barge, P.; Sommeria, J., Did planet formation begin inside persistent gaseous vortices?, A&A, L1-L4 (1995)
[7] Barranco, J.; Marcus, P.; Umurhan, O., Scaling & asymptotics of coherent vortices in protoplanetary disks, (Proceedings of the 2000 Summer Program - Center for Turbulence Research (2001), Stanford University Press), 85-96
[8] Barranco, J.; Marcus, P., Vortices in protoplanetary disks & the formation of planetesimals, (Proceedings of the 2000 Summer Program - Center for Turbulence Research (2001), Stanford University Press), 97-108
[9] Barranco, J.; Marcus, P., Three-dimensional vortices in stratified protoplanetary disks, Astrophys. J., 623, 1157-1170 (2005)
[10] Brown, P.; Cooke, B., Model predictions for the 2001 Leonids and implications for Earth-orbiting satellites, Monthly Notices Royal Astronom. Soc., 326, L19-L22 (2001)
[11] Beckwith, S.; Henning, T.; Nakagawa, Y., Dust particles in protoplanetary disks, (Mannings, V.; Boss, A. P.; Russell, S. S., Protostars & Planets IVs (2000), University of Arizona Press: University of Arizona Press Tuscon)
[12] Benz, W., From dust to planets, Spatium, 6, 3-14 (2000)
[13] Benz, W., Impact simulations with fracture. 1. Method & tests, Icarus, 107, 98-116 (1994)
[14] Berger, S. A.; Jou, L. D., Flow in stenotic vessels, Ann. Rev. Fluid Mech., 32, 347-382 (2000) · Zbl 0989.76096
[15] L. Berlyand, A. Panchenko, Strong and weak blow up of the viscous dissipation rates for concentrated suspensions, J. Fluid Mech., in press.; L. Berlyand, A. Panchenko, Strong and weak blow up of the viscous dissipation rates for concentrated suspensions, J. Fluid Mech., in press. · Zbl 1127.76067
[16] Berlyand, L.; Panchenko, A., Network approximation for effective viscosity of concentrated suspensions with complex geometries, SIAM J. Math. Anal., 36, 5, 1580-1628 (2005) · Zbl 1130.76082
[17] Blum, J.; Wurm, G., Impact simulations on sticking, restructuring, & fragmentation of preplanetary dust aggregates, Icarus, 143, 138-146 (2000)
[18] Bohren, C.; Huffman, D., Absorption and Scattering of Light by Small Particles (1998), Wiley Science Paperback Series
[19] Cho, H.; Barber, J. R., Stability of the three-dimensional Coloumb friction law, Proc. Royal Soc., 455, 1983, 839-862 (1999) · Zbl 0947.74038
[20] Chokshi, A.; Tielens, A. G.G. M.; Hollenbach, D., Dust coagulation, Astrophys. J., 407, 806-819 (1993)
[21] Chow, C. Y., An Introduction to Computational Fluid Dynamics (1980), Wiley: Wiley New York
[22] Chyu, K. Y.; Shah, P. K., The role of inflammation in plaque disruption and thrombosis, Rev. Cardiovas. Med., 2, 82-91 (2001)
[23] Cuzzi, C. N.; Dobrovolskis, A. R.; Champney, J. M., Particle-gas dynamics in the midplane of a protoplanetary nebula, Icarus, 106, 102-134 (1993)
[24] Davies, M. J.; Richardson, P. D.; Woolf, N.; Katz, D. R.; Mann, J., Risk of thrombosis in human atherosclerotic plaques: role of extracellular lipid, macrophage, and smooth muscle cell content, Br. Heart J., 69, 377-381 (1993)
[25] Dominik, C.; Tielens, A. G.G. M., The physics of dust coagulation & the structure of dust aggregates in space, Astrophys. J., 480, 647-673 (1997)
[26] I. St. Doltsinis, Coupled field problems-solution techniques for sequential & parallel processing, in: M. Papadrakakis (Ed.), Solving Large-scale Problems in Mechanics, 1993.; I. St. Doltsinis, Coupled field problems-solution techniques for sequential & parallel processing, in: M. Papadrakakis (Ed.), Solving Large-scale Problems in Mechanics, 1993.
[27] Doltsinis, I. St., Solution of coupled systems by distinct operators, Engrg. Comput., 14, 829-868 (1997) · Zbl 0983.65502
[28] Donev, A.; Cisse, I.; Sachs, D.; Variano, E. A.; Stillinger, F.; Connelly, R.; Torquato, S.; Chaikin, P., Improving the density of jammed disordered packings using ellipsoids, Science, 303, 990-993 (2004)
[29] Donev, A.; Torquato, S.; Stillinger, F., Neighbor list collision-driven molecular dynamics simulation for nonspherical hard particles-I. Algorithmic details, J. Comput. Phys., 202, 737 (2005) · Zbl 1067.82061
[30] Donev, A.; Torquato, S.; Stillinger, F., Neighbor list collision-driven molecular dynamics simulation for nonspherical hard particles-II. Application to ellipses and ellipsoids, J. Comput. Phys., 202, 765 (2005) · Zbl 1067.82062
[31] Druzhinin, O. A.; Elghobashi, S. E., Direct numerical simulation of a three-dimensional spatially-developing bubble-laden mixing layer with two-way coupling, J. Fluid Mech., 429, 23-61 (2001) · Zbl 1007.76087
[32] Farhat, C.; Lesoinne, M.; Maman, N., Mixed explicit/implicit time integration of coupled aeroelastic problems: three-field formulation, geometric conservation and distributed solution, Int. J. Numer. Methods Fluids, 21, 807-835 (1995) · Zbl 0865.76038
[33] Farhat, C.; Lesoinne, M., Two efficient staggered procedures for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems, Comput. Methods Appl. Mech. Engrg., 182, 499-516 (2000) · Zbl 0991.74069
[34] Farhat, C.; van der Zee, G.; Geuzaine, P., Provably second-order time-accurate loosely-coupled solution algorithms for transient nonlinear computational aeroelasticity, Comput. Methods Appl. Mech. Engrg., 195, 1973-2001 (2006) · Zbl 1178.76259
[35] Ferrante, A.; Elghobashi, S. E., On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence, Phys. Fluids, 15, 315-329 (2003) · Zbl 1185.76126
[36] Frenklach, M.; Carmer, C. S., Molecular dynamics using combined quantum & empirical forces: application to surface reactions, Adv. Classical Trajectory Methods, 4, 27-63 (1999)
[37] Fuster, V., Assessing and Modifying the Vulnerable Atherosclerotic Plaque (2002), Futura Publishing Company
[38] W. Goldsmith, Impact: The Theory & Physical Behavior of Colliding Solids, Dover Re-issue, Toronto, 2001.; W. Goldsmith, Impact: The Theory & Physical Behavior of Colliding Solids, Dover Re-issue, Toronto, 2001. · Zbl 0986.74001
[39] Grazier, K. R.; Newman, W. I.; Kaula, W. M.; Hyman, J. M., Dynamical evolution of planetesimals in the outer solar system I. The Jupiter/Saturn zone, Icarus, 140, 2, 341-352 (2000)
[40] Grazier, K. R.; Newman, W. I.; Varadi, F.; Kaula, W. M.; Hyman, J. M., Dynamical evolution of planetesimals in the outer solar system II. The Saturn/Uranus & Uranus/Neptune zones, Icarus, 140, 2, 353-368 (1999)
[41] Haile, J. M., Molecular Dynamics Simulations: Elementary Methods (1992), Wiley
[42] Hale, J.; Kocak, H., Dynamics & Bifurcations (1991), Springer-Verlag · Zbl 0745.58002
[43] Hase, W. L., Molecular Dynamics of Clusters, Surfaces, Liquids, & Interfaces, Advances in Classical Trajectory Methods, vol. 4 (1999), JAI Press
[44] Johnson, K., Contact Mechanics (1985), Cambridge University Press · Zbl 0599.73108
[45] Jou, L. D.; Berger, S. A., Numerical simulation of the flow in the carotid bifurcation, Theor. Comput. Fluid Mech., 10, 239-248 (1998) · Zbl 0912.76043
[46] Kansaal, A.; Torquato, S.; Stillinger, F., Diversity of order and densities in jammed hard-particle packings, Phys. Rev. E, 66, 041109 (2002)
[47] Kikuchi, N.; Oden, J. T., Contact Problems in Elasticity: A Study of Variational Inequalities & Finite Element Methods (1988), SIAM: SIAM Philadelphia, PA · Zbl 0685.73002
[48] Klarbring, A., Examples of nonuniqueness & nonexistence of solutions to quasistatic contact problems with friction, Ingenieur-Archiv., 60, 529-541 (1990)
[49] Kokubo, E.; Ida, S., Formation of protoplanets from planetesimals in the solar nebula, Icarus, 143, 1, 15-270 (2000)
[50] Kokubo, E.; Ida, S., On runaway growth of planetesimals, Icarus, 123, 1, 180-191 (1996)
[51] Lesoinne, M.; Farhat, C., Free staggered algorithm for nonlinear transient aeroelastic problems, AIAA J., 36, 9, 1754-1756 (1998)
[52] Le Tallec, P.; Mouro, J., Fluid structure interaction with large structural displacements, Comput. Methods Appl. Mech. Engrg., 190, 24-25, 3039-3067 (2001) · Zbl 1001.74040
[53] Lewis, R. W.; Schrefler, B. A., The Finite Element Method in the Static & Dynamic Deformation & Consolidation of Porous Media (1998), Wiley Press · Zbl 0935.74004
[54] Lewis, R. W.; Schrefler, B. A.; Simoni, L., Coupling versus uncoupling in soil consolidation, Int. J. Numer. Anal. Methods Geomech., 15, 533-548 (1992)
[55] Libby, P., Current concepts of the pathogenesis of the acute coronary syndromes, Circulation, 104, 365-372 (2001)
[56] Libby, P., The vascular biology of atherosclerosis, (Braunwald, E.; Zipes, D. P.; Libby, P., Heart Disease. A Textbook of Cardiovascular Medicine, sixth (2001), W.B. Saunders Company: W.B. Saunders Company Philadelphia), 995-1009, Chapter 30
[57] Libby, P.; Ridker, P. M.; Maseri, A., Inflammation and Atherosclerosis, Circulation, 105, 1135-1143 (2002)
[58] Libby, P.; Aikawa, M., Stabilization of atherosclerotic plaques: new mechanisms and clinical targets, Nat. Med., 8, 1257-1262 (2002)
[59] Lissauer, J. J., Planet formation, ARAA, 31, 129-174 (1993)
[60] Loree, H. M.; Kamm, R. D.; Stringfellow, R. G.; Lee, R. T., Effects of fibrous cap thickness on peak circumferential stress in model atherosclerotic vessels, Circ. Res., 71, 850-858 (1992)
[61] Luo, L.; Dornfeld, D. A., Material removal mechanism in chemical mechanical polishing: theory and modeling, IEEE Trans.: Semicond. Manufactur., 14, 2, 112-133 (2001)
[62] Luo, L.; Dornfeld, D. A., Effects of abrasive size distribution in chemical-mechanical planarization: modeling and verification, IEEE Trans.: Semicond. Manufactur., 16, 469-476 (2003)
[63] Luo, L.; Dornfeld, D. A., Material removal regions in chemical mechanical planarization for sub-micron integration for sub-micron integrated circuit fabrication: coupling effects of slurry chemicals, abrasive size distribution, and wafer-pad contact area, IEEE Trans.: Semicond. Manufactur., 16, 45-56 (2003)
[64] Luo, L.; Dornfeld, D. A., Integrated Modeling of Chemical Mechanical Planarization of Sub-micron IC Fabrication (2004), Springer-Verlag
[65] Martins, J. A.C.; Oden, J. T., Existence & uniqueness results in dynamics contact problems with nonlinear normal & friction interfaces, Nonlinear Anal., 11, 407-428 (1987) · Zbl 0672.73079
[66] Mitchell, P.; Frenklach, M., Particle Aggregation with Simultaneous Surface Growth, Phys. Rev. E, 67, 061407 (2003)
[67] Moelwyn-Hughes, E. A., Physical Chemistry (1961), Pergamon
[68] Oden, J. T.; Pires, E., Nonlocal & nonlinear friction laws & variational principles for contact problems in elasticity, ASME J. Appl. Mech., 50, 67-76 (1983) · Zbl 0515.73121
[69] Pollack, J. N.; Hollenbach, D.; Beckwith, S.; Simonelli, D. P.; Roush, T.; Fong, W., Composition & radiative properties in molecular clouds & accretion disks, Astrophys. J., 421, 615-639 (1994)
[70] K.C. Park, C.A. Felippa, Partitioned analysis of coupled systems, in: T. Belytschko, T.J.R. Hughes (Eds.), Computational Methods for Transient Analysis, 1983.; K.C. Park, C.A. Felippa, Partitioned analysis of coupled systems, in: T. Belytschko, T.J.R. Hughes (Eds.), Computational Methods for Transient Analysis, 1983. · Zbl 0546.73063
[71] Piperno, S., Explicit/implicit fluid/structure staggered procedures with a structural predictor & fluid subcycling for 2D inviscid aeroelastic simulations, Int. J. Numer. Meth. Fluids, 25, 1207-1226 (1997) · Zbl 0910.76065
[72] Piperno, S.; Farhat, C.; Larrouturou, B., Partitioned procedures for the transient solution of coupled aeroelastic problems - Part I: Model problem, theory, and two-dimensional application, Comput. Methods Appl. Mech. Engrg., 124, 1-2, 79-112 (1995) · Zbl 1067.74521
[73] Piperno, S.; Farhat, C., Partitioned procedures for the transient solution of coupled aeroelastic problems - Part II: Energy transfer analysis and three-dimensional applications, Comput. Methods Appl. Mech. Engrg., 190, 3147-3170 (2001) · Zbl 1015.74009
[74] Rapaport, D. C., The Art of Molecular Dynamics Simulation (1995), Cambridge University Press · Zbl 0612.65004
[75] Richardson, P. D.; Davies, M. J.; Born, G. V.R., Influence of plaque configuration and stress distribution on fissuring of coronary atherosclerotic plaques, Lancet, 2, 8669, 941-944 (1989)
[76] Schlick, T., Molecular Modeling & Simulation, An Interdisciplinary Guide (2000), Springer-Verlag: Springer-Verlag New York
[77] Schmidt, L., The Engineering of Chemical Reactions (1998), Oxford University Press
[78] Schrefler, B. A., A partitioned solution procedure for geothermal reservoir analysis, Comm. Appl. Num. Meth., 1, 53-56 (1985) · Zbl 0587.76150
[79] Shah, P. K., Plaque disruption and coronary thrombosis: new insight into pathogenesis and prevention, Clinical Cardiol., 20, suppl. II, II-38-II-44 (1997)
[80] Stillinger, F. H.; Weber, T. A., Computer simulation of local order in condensed phases of silicon, Phys. Rev. B, 31, 5262-5271 (1985)
[81] Stroud, J. S.; Berger, S. A.; Saloner, D., Numerical analysis of flow through a severely stenotic carotid artery bifurcation, J. Biomed. Engrg., 124, 1, 9-21 (2002)
[82] Stroud, J. S.; Berger, S. A.; Saloner, D., Influence of stenosis morphology on flow through severely stenotic vessels: implications of plaque rupture, J. Biomech., 33, 443-455 (2000)
[83] Supulver, K. D.; Lin, D. N.C., Formation of icy planetesimals in a turbulent solar nebula, Icarus, 146, 2, 525-540 (2000)
[84] Tanga, P.; Babiano, A.; Dubrulle, B.; Provenzale, A., Forming planetesimals in vortices, Icarus, 121, 1, 158-170 (1996)
[85] Torquato, S., Random Heterogeneous Materials: Microstructure and Macroscopic Properties (2002), Springer-Verlag: Springer-Verlag New York · Zbl 0988.74001
[86] Tersoff, J., Empirical interatomic potential for carbon, with applications to amorphous carbon, Phys. Rev. Lett., 61, 2879-2882 (1988)
[87] van der Wal, A. C.; Becker, A. E., Atherosclerotic plaque rupture – pathologic basis of plaque stability and instability, Cardiovasc. Res., 41, 334-344 (1999)
[88] Weidenschilling, S. J.; Cuzzi, J. N., Formation of planetesimals in the solar nebula, (Levy, E. H.; Lunine, J. I., Protostars & Planets III (1993), University of Arizona Press: University of Arizona Press Tucson), 1031-1060
[89] Weidenschilling, S. J.; Spaute, D.; Davis, D. R.; Marzari, F.; Ohtsuki, K., Accretional evolution of a planetesimal swarm, Icarus, 128, 2, 429-455 (1997)
[90] Widom, B., Random sequential addition of hard spheres to a volume, J. Chem. Phys., 44, 3888-3894 (1966)
[91] Wriggers, P., Computational Contact Mechanics (2002), John-Wiley
[92] Wurm, G.; Blum, J.; Colwell, J. E., A new mechanism relevant to the formation of planetesimals in the solar nebula, Icarus, 151, 318-321 (2001)
[93] Zienkiewicz, O. C., Coupled problems & their numerical solution, (Lewis, R. W.; Bettes, P.; Hinton, E., Numerical Methods in Coupled Systems (1984), Wiley: Wiley Chichester), 35-58 · Zbl 0548.73048
[94] Zohdi, T. I., An adaptive-recursive staggering strategy for simulating multifield coupled processes in microheterogeneous solids, Int. J. Numer. Methods Engrg., 53, 1511-1532 (2002) · Zbl 1114.74496
[95] Zohdi, T. I., Modeling and simulation of a class of coupled thermo-chemo-mechanical processes in multiphase solids, Comput. Methods Appl. Mech. Engrg., 193, 6-8, 679-699 (2004) · Zbl 1060.74528
[96] Zohdi, T. I., Modeling and direct simulation of near-field granular flows, Int. J. Solids Struct., 42/2, 539-564 (2004) · Zbl 1081.74012
[97] Zohdi, T. I., A computational framework for agglomeration in thermo-chemically reacting granular flows, Proc. Royal Soc., 460, 2052, 3421-3445 (2004) · Zbl 1070.76057
[98] Zohdi, T. I., Charge-induced clustering in multifield granular flow, Int. J. Numer. Methods Engrg., 62, 7, 870-898 (2005) · Zbl 1161.74355
[99] Zohdi, T. I.; Holzapfel, G. A.; Berger, S. A., A phenomenological model for atherosclerotic plaque growth and rupture, J. Theor. Biol., 227, 3, 437-443 (2004) · Zbl 1439.92072
[100] Zohdi, T. I., A simple model for shear stress mediated lumen reduction in blood vessels, Biomech. Model. Mechanobiol., 4, 1, 57-61 (2005)
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