# Numerical simulation of gluey particles

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

- Volume: 43, Issue: 1, page 53-80
- ISSN: 0764-583X

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topLefebvre, Aline. "Numerical simulation of gluey particles." ESAIM: Mathematical Modelling and Numerical Analysis 43.1 (2008): 53-80. <http://eudml.org/doc/194447>.

@article{Lefebvre2008,

abstract = {
We propose here a model and a numerical scheme to compute the motion
of rigid particles interacting through the lubrication force. In the
case of a particle approaching a plane, we propose an algorithm and
prove its convergence towards the solutions to the gluey particle model
described in [B. Maury, ESAIM: Proceedings18 (2007)
133–142]. We propose a multi-particle version of
this gluey model which is based on the projection of the velocities
onto a set of admissible velocities. Then, we describe a multi-particle algorithm
for the simulation of such systems and present numerical results.
},

author = {Lefebvre, Aline},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Fluid/particle systems; fluid/solid interaction;
lubrication force; contacts; Stokes fluid.; lubrication force; Stokes fluid; multi-particle algorithm},

language = {eng},

month = {10},

number = {1},

pages = {53-80},

publisher = {EDP Sciences},

title = {Numerical simulation of gluey particles},

url = {http://eudml.org/doc/194447},

volume = {43},

year = {2008},

}

TY - JOUR

AU - Lefebvre, Aline

TI - Numerical simulation of gluey particles

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2008/10//

PB - EDP Sciences

VL - 43

IS - 1

SP - 53

EP - 80

AB -
We propose here a model and a numerical scheme to compute the motion
of rigid particles interacting through the lubrication force. In the
case of a particle approaching a plane, we propose an algorithm and
prove its convergence towards the solutions to the gluey particle model
described in [B. Maury, ESAIM: Proceedings18 (2007)
133–142]. We propose a multi-particle version of
this gluey model which is based on the projection of the velocities
onto a set of admissible velocities. Then, we describe a multi-particle algorithm
for the simulation of such systems and present numerical results.

LA - eng

KW - Fluid/particle systems; fluid/solid interaction;
lubrication force; contacts; Stokes fluid.; lubrication force; Stokes fluid; multi-particle algorithm

UR - http://eudml.org/doc/194447

ER -

## References

top- Y. Achdou, O. Pironneau and F. Valentin, Effective boundary conditions for laminar flows over periodic rough boundaries. J. Comp. Phys.147 (1998) 187–218.
- Y. Assou, D. Joyeux, A. Azouni and F. Feuillebois, Mesure par interférométrie laser du mouvement d'une particule proche d'une paroi. J. Phys. III1 (1991) 315–330.
- L. Bocquet and J.-L. Barrat, Hydrodynamic boundary conditions, correlation functions, and Kubo relations for confined fluids. Phys. Rev. E49 (1994) 3079–3092.
- J.F. Brady and G. Bossis, Stokesian dynamics. Ann. Rev. Fluid Mech.20 (1988) 111–157.
- D. Bresh and V. Milisic, High order multi-scale wall-laws, part I: The periodic case. Quat. Appl. Math. (to appear) v2. URIArXiv:math/0611083
- R.G. Cox, The motion of suspended particles almost in contact. Int. J. Multiphase Flow1 (1974) 343–371.
- R.G. Cox and H. Brenner, The slow motion of a sphere through a viscous fluid towards a plane surface – II – Small gap width, including inertial effects. Chem. Engng. Sci.22 (1967) 1753–1777.
- S.L. Dance and M.R. Maxey, Incorporation of lubrication effects into the force-coupling method for particulate two-phase flow. J. Comp. Phys.189 (2003) 212–238.
- B. Desjardin and M.J. Esteban, Existence of weak solutions for the motion of rigid bodies in a viscous fluid. Arch. Ration. Mech. Anal.146 (1999) 59–71.
- A. Einstein, A new method of determining molecular dimensions. Ann. Phys. Leipsig19 (1906) 289–306.
- A. Einstein, Correction to my work: a new determination of molecular dimensions. Ann. Phys. Leipsig34 (1911) 591–592.
- E. Feireisl, On the motion of rigid bodies in a viscous incompressible fluid. J. Evol. Equ.3 (2003) 419–441.
- R. Glowinski, T.-W. Pan, T.I. Heslaand and D.D. Joseph, A distributed Lagrange multiplier/fictitious domain method for particulate flows. Int. J. Multiphase Flow25 (1999) 755–794.
- M. Hillairet, Lack of collision between solid bodies in a 2D constant-density incompressible viscous flow. Comm. Partial Diff. Eq.32 (2007) 1345–1371.
- H.H. Hu, Direct simulation of flows of solid-liquid mixtures. Int. J. Multiphase Flow22 (1996) 335–352.
- A.A. Johnson and T.E. Tezduyar, Simulation of multiple spheres falling in a liquid-filled tube. Comput. Methods Appl. Mech. Engrg.134 (1996) 351–373.
- S. Labbé, J. Laminie and V. Louvet, CSiMoon. Calcul scientifique, méthodologie orientée objet et environnement: de l'analyse mathématique à la programmation. Technical report RT 2001-01, Laboratoire de Mathématiques, Université Paris-Sud, France (2004).
- N. Lecocq, F. Feuillebois, N. Anthore, R. Anthore, F. Bostel and C. Petipas, Precise measurement of particle-wall hydrodynamic interactions at low Reynolds number using laser interferometry. Phys. Fluids A5 (1993) 3–12.
- N. Lecoq, R. Anthore, B. Cichocki, P. Szymczak and F. Feuillebois, Drag force on a sphere moving towards a corrugated wall. J. Fluid Mech.513 (2004) 247–264.
- A. Lefebvre, Fluid-Particle simulations with FreeFem++, in ESAIM: Proceedings18, J.-F. Gerbeau and S. Labbé Eds. (2007) 120–132.
- A. Lefebvre, Simulation numérique d'écoulements fluide/particules. Ph.D. thesis, Université Paris-Sud XI, Orsay, France (Nov. 2007).
- B. Maury, A many-body lubrication model. C.R. Acad. Sci. Paris325 (1997) 1053–1058.
- B. Maury, Direct simulation of 2D fluid-particle flows in biperiodic domains. J. Comp. Phys.156 (1999) 325–351.
- B. Maury, A time-stepping scheme for inelastic collisions. Numer. Math.102 (2006) 649–679.
- B. Maury, A gluey particle model, in ESAIM: Proceedings18, J.-F. Gerbeau and S. Labbé Eds. (2007) 133–142.
- S. Nasseri, N. Phan-Thien and X.J. Fan, Lubrication approximation in completed double layer boundary element method. Comput. Mech.26 (2000) 388–397.
- N.A. Patankar, P. Singh, D.D. Joseph, R. Glowinski and T.-W. Pan, A new formulations for the distributed Lagrange multiplier/fictitious domain method for particulate flows. Int. J. Multiphase Flow26 (2000) 1509–1524.
- S. Richardson, A model for the boundary condition of a porous material. Part 2. J. Fluid Mech.49 (1971) 327–336.
- J.A. San Matín, V. Starovoitov and M. Tucsnak, Global weak solutions for the two-dimensional motion of several rigid bodies in an incompressible viscous fluid. Arch. Ration. Mech. Anal.161 (2002) 113–147.
- P. Singh, T.I. Hesla and D.D. Joseph, Distributed Lagrange multiplier method for particulate flows with collisions. Int. J. Multiphase Flow29 (2003) 495–509.
- J.R. Smart and D.T. Leighton, Measurement of the hydrodynamic roughness of non colloidal spheres. Phys. Fluids A1 (1989) 52.
- D.E. Stewart, Rigid-body dynamics with friction and impact. SIAM Rev.42 (2000) 3–39.
- T. Takahashi, Analysis of strong solutions for the equations modeling the motion of a rigid-fluid system in a bounded domain. Adv. Differential Equations8 (2003) 1499–1532.
- T. Takahashi, Existence of strong solutions for the problem of a rigid-fluid system. C.R. Math. Acad. Sci. Paris336 (2003) 453–458.
- G.I. Taylor, A model for the boundary condition of a porous material. Part 1. J. Fluid Mech.49 (1971) 319–326.
- O.I. Vinogradova and G.E. Yacubov, Surface roughness and hydrodynamic boundary conditions. Phys. Rev. E73 (2006) 045302(R).
- D. Wan and S. Turek, Direct numerical simulation of particulate flow via multigrid FEM techniques and the fictitious boundary method. Int. J. Numer. Meth. Fluids51 (2006) 531–566.

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