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Three-dimensional vortex methods for particle-laden flows with two-way coupling. (English) Zbl 1014.76067

From the summary: This paper presents a three-dimensional viscous vortex method for simulation of particulate flows with two-way coupling. The flow is computed using Lagrangian vortex elements advected with local velocity, while their strength is modified to account for viscous diffusion, vortex stretching, and generating vorticity induced by the particles. The solid particles move according to viscous drag and gravity, creating vorticity which is discretised using vortex elements. This method adaptively tracks the evolution of vorticity field and the generation of new computational elements to account for the vorticity source term. A key aspect of the present scheme is the remeshing of computational elements to adaptively accommodate the production of vorticity induced by solid particles, and to ensure sufficient support for the proper resolution of diffusion equation.

MSC:

76M23 Vortex methods applied to problems in fluid mechanics
76T15 Dusty-gas two-phase flows
76R50 Diffusion

References:

[1] Baker, Gregory R.; Meiron, Daniel I.; Orszag, Steven A., Vortex simulations of the Rayleigh-Taylor instability, Phys. Fluids, 23, 1485 (1980) · Zbl 0439.76034
[2] Batchelor, G. K.; Nitsche, J. M., Expulsion of particles from a buoyant blob in a fludized bed, J. Fluid Mech., 278, 63 (1994)
[3] Beale, J. Thomas; Majda, Andrew, Vortex methods. II. Higher order accuracy in two and three dimensions, Math. Comput., 39, 29 (1982) · Zbl 0488.76025
[4] Birdsall, Charles K.; Fuss, Dieter, Clouds-in-clouds, clouds-in-cells physics for many-body plasma simulation, J. Comput. Phys., 3, 494 (1969) · Zbl 0938.76088
[5] Brecht, Stephen G.; Ferrante, John. R., Vortex-in-cell calculations in three dimensions, Comput. Phys. Commun., 58, 25 (1990)
[6] Brecht, Stephen H.; Ferrante, John R., Vortex-in-cell simulation of buoyant bubbles in three dimensions, Phys. Fluids A, 1, 1166 (1989) · Zbl 0673.76108
[7] Chein, Reiyu; Chung, J. N., Simulation of particle dispersion in a two-dimensional mixing layer, AIChe J., 34, 946 (1998)
[8] Chen, H.; Marshall, J. S., A Lagrangian vorticity method for two-phase particulate flows with two-way phase coupling, J. Comput. Phys., 148, 169 (1999) · Zbl 0931.76068
[9] Cheng, H.; Greengard, L.; Rokhlin, V., A fast adaptive multipole algorithm in three dimensions, J. Comput. Phys., 155, 468 (1999) · Zbl 0937.65126
[10] Childress, S.; Peyret, R., A numerical study of two-dimensional convection by motile particles, J. Mec., 15, 753 (1976) · Zbl 0356.76005
[11] Chorin, Alexandre Joel, Hairpin removal in vortex interactions, J. Comput. Phys., 91, 1 (1990) · Zbl 0711.76047
[12] Christiansen, J. P., Numerical simulation of hydrodynamics by the method of point vortices, J. Comput. Phys., 13, 363 (1973) · Zbl 0267.76009
[13] Cottet, G.-H., artifical viscosity models for vortex and particle methods, J. Comput. Phys., 127, 299 (1996) · Zbl 0860.76065
[14] G.-H. Cottet, Personal communication, 1999.; G.-H. Cottet, Personal communication, 1999.
[15] Cottet, G.-H.; Koumoutsakos, P., Vortex Methods: Theory and Practice (2000)
[16] Crowe, C. T.; Troutt, T. R.; Chung, J. N., Numerical models for two-phase turbulent flows, Annu. Rev. Fluid Mech., 28, 11 (1996)
[17] Degond, P.; Mas-Gallic, S., The weighted particle method for convection-diffusion equations. 1. The case of an isotropic viscosity, Math. Comput., 53, 485 (1989) · Zbl 0676.65121
[18] Eaton, J. K.; Fessler, J. R., Preferential concentration of particles by turbulence, Int. J. Multiphase Flow., 20, 169 (1994) · Zbl 1134.76536
[19] Feynman, R. P., Application of quantum mechanics to liquid helium, Prog. Low Temp. Phys., 1, 17 (1955)
[20] Fletcher, C. A.J., Computational Techniques for Fluid Dynamics. Fundamental and General Techniques, I (1991) · Zbl 0706.76001
[21] Glowinski, Roland; Pan, Tsorng-Whay; Hesla, Todd I.; Joseph, Daniel D.; Periaux, Jacques, A distributed Lagrange multiplier/fictitious domain method for flows aound moving rigid bodies: Application to particulate flow, Int. J. Numer. Methods Fluids, 30, 1043 (1999) · Zbl 0971.76046
[22] Hald, Ole H., Convergence of vortex methods for Euler’s equations, II, SIAM J. Numer. Anal., 16, 726 (1979) · Zbl 0427.76024
[23] Hockney, R. W.; Eastwood, J. W., Computer Simulation Using Particles (1988) · Zbl 0662.76002
[24] Hunt, J. C.R., Industrial and environmental fluid mechanics, Annu. Rev. Fluid Mech., 23, 1 (1991) · Zbl 1125.76300
[25] Kerr, Robert M., Simulation of Rayleigh-Taylor flows using vortex blobs, J. Comput. Phys., 76, 48 (1988) · Zbl 0638.76057
[26] Knio, Omar M.; Ghoniem, Ahmed F., Three-dimensional vortex simulation of rollup and entranment in a shear layer, J. Comput. Phys., 97, 172 (1991) · Zbl 0737.76011
[27] Koumoutsakos, P., Inviscid axisymmetrization of an elliptical vortex ring, J. Comput. Phys., 138, 821 (1997) · Zbl 0902.76080
[28] Leonard, A., Vortex methods for flow simulations, J. Comput. Phys., 37, 289 (1980) · Zbl 0438.76009
[29] Li, C. W., Convection of particle thermals (convection de nuages de particules), J. Mec., 35, 363 (1997)
[30] Lundgren, T. S., Slow flow through stationary random beads and suspensions of spheres, J. Fluid Mech., 51, 273 (1972) · Zbl 0229.76067
[31] Mansfield, John R.; Knio, Omar M.; Meneveau, Charles, Dynamics LES of colliding vortex rings using a 3Df vortex method, J. Comput. Phys., 152, 305 (1999) · Zbl 0947.76041
[32] Martin, J. E.; Meiburg, E., The accumulation and dispersion of heavy particles in forced two-dimensional mixing layers. I. The fundamental an subharmonic cases, Phys. Fluids, 6, 1116 (1994) · Zbl 0829.76091
[33] Maxey, M. R.; Riley, J. J., Equation of motion for a small rigid sphere in a non-uniform flow, Phys. Fluids A, 26, 883 (1983) · Zbl 0538.76031
[34] Mitts, Chad J., An Investigation of Transcritical Droplet Dynamics through the Use of a Miscible Fluid Analog (1996)
[35] Monaghan, J. J., Extrapolating B splines for interpolation, J. Comput. Phys., 200, 253 (1985) · Zbl 0588.41005
[36] Nitsche, J. M.; Batchelor, G. K., Break-up of a falling drop containing dispersed particles, J. Fluid Mech., 340, 161 (1997) · Zbl 0892.76020
[37] Oseen, C. W., Neuere Methoden und Ergebnisse in der Hydrodynamik (1927) · JFM 53.0773.02
[38] Poletto, Massimo; Joseph, Daniel D., Effective density an viscosity of a suspension, J. Rheol., 39, 323 (1995)
[39] Powell, R. L.; Mason, S. G., Dispersion by laminar flow, AIChe J., 28, 286 (1982)
[40] Raviart, P. A., An Analysis of Particle Methods, 1127, 243 (1983) · Zbl 0598.76003
[41] Saffman, P. G., Vortex Dynamics (1992) · Zbl 0777.76004
[42] J. T. Sagredo, J. H. Walther, and, P. Koumoutsakos, High resolution vortex-in-cell methods, submitted for publication.; J. T. Sagredo, J. H. Walther, and, P. Koumoutsakos, High resolution vortex-in-cell methods, submitted for publication. · Zbl 1172.76351
[43] Crayfishpak. User’s Guide (1990)
[44] Sundaram, Shivshankar; R. Collins, Lance, Numerical considerations in simulating a turbulent suspension of finite-volume particles, J. Comput. Phys., 124, 337 (1996) · Zbl 0849.76054
[45] Sundaram, Shivshankar; Collins, Lance R., A numerical study of the modulation of isotropic turbulence by suspended particles, J. Fluid Mech., 379, 105 (1999) · Zbl 0938.76045
[46] Tang, L.; Wen, F.; Yang, Y.; Crowe, C. T.; Chung, J. N.; Troutt, T. R., Self-organizing particle dispersion mechanisms in a plane wake, Phys. Fluids A, 4, 2244 (1992)
[47] Thompson, D’Arcy Wentworth, On Growth and Form (1992) · Zbl 0063.07372
[48] Thomson, J. J.; Newall, H. F., On the formation of vortex rings by drops falling into liquids, and some allied phenomena, Proc. R. Soc., 39, 417 (1885)
[49] Tryggvason, Grétar, Numerical simulations of the Rayleigh-Taylor instability, J. Comput. Phys., 75, 253 (1988) · Zbl 0638.76056
[50] Williamson, J. H., Low-storage runge-kutta schemes, J. Comput. Phys., 35, 48 (1980) · Zbl 0425.65038
[51] Zufiria, Juan A., Vortex-in-cell simulation of bubble competition in Rayleigh-Taylor instability, Phys. Fluids, 31, 3199 (1988) · Zbl 0654.76095
[52] Zufiria, Juan A., Linear analysis of the vortex-in-cell algorithm applied to Rayleigh-Taylor instability, J. Comput. Phys., 80, 387 (1989) · Zbl 0659.76049
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