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On discretization in time in simulations of particulate flows
1. | Ceremade, UMR CNRS 7534, Université Dauphine, Place du Maréchal De Lattre De Tassigny, F-75016 Paris, France |
2. | Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse et CNRS, 118 route de Narbonne, F-31062 Toulouse Cedex 9, France |
3. | Institut de Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, 7 rue René Descartes, F-67084 Strasbourg Cedex, France |
References:
[1] |
J. F. Brady and G. Bossis, Stokesian dynamics, Annual Review of Fluid Mechanics, 20 (1988), 111-157.
doi: oi:10.1146/annurev.fl.20.010188.000551. |
[2] |
J. Butcher, "Numerical Methods for Ordinary Differential Equations," John Wiley & Sons Ltd., Chichester, 2003.
doi: doi:10.1002/0470868279. |
[3] |
M. Cooley and M. O'Neill, On the slow motion generated in a viscous fluid by the approach of a sphere to a plane wall or stationary sphere, Mathematika, 16 (1969), 37-49.
doi: doi:10.1112/S0025579300004599. |
[4] |
S. L. Dance and M. R. Maxey, Incorporation of lubrication effects into the force-coupling method for particulate two-phase flow, Journal of Computational Physics, 189 (2003), 212-238.
doi: doi:10.1016/S0021-9991(03)00209-2. |
[5] |
W. R. Dean and M. E. O'Neill, A slow motion of viscous liquid caused by the rotation of a solid sphere, Mathematika, 10 (1963), 13-24.
doi: doi:10.1112/S0025579300003314. |
[6] |
G. P. Galdi, "An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Vol. I, Linearized Steady Problems," vol. 38 of Springer Tracts in Natural Philosophy, Springer-Verlag, New York, 1994. |
[7] |
D. Gérard-Varet and M. Hillairet, Regularity issues in the problem of fluid structure interaction, Arch. Ration. Mech. Anal., 195 (2010), 375-407.
doi: doi:10.1007/s00205-008-0202-9. |
[8] |
R. Glowinski, T.-W. Pan, T. I. Hesla and D. D. Joseph, A distributed lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiphase Flow, 24 (1999), 755-794.
doi: doi:10.1016/S0301-9322(98)00048-2. |
[9] |
F. Hecht, O. Pironneau, A. L. Hyaric and K. Ohtsuka, Freefem++, ver. 3.7, http://www.freefem.org/ff++, (2009). |
[10] |
M. Hillairet, Lack of collision between solid bodies in a 2D incompressible viscous flow, Comm. Partial Differential Equations, 32 (2007), 1345-1371.
doi: doi:10.1080/03605300601088740. |
[11] |
M. Hillairet and T. Takahashi, Collisions in three-dimensional fluid structure interaction problems, SIAM J. Math. Anal., 40 (2009), 2451-2477.
doi: doi:10.1137/080716074. |
[12] |
M. S. Ingber, A. Mammoli, P. Vorobieff, T. McCollam and A. Graham, Experimental and numerical analysis of irreversibilities among particles suspended in a couette device, Journal of Rheology, 50 (2006), 99-114.
doi: doi:10.1122/1.2169806. |
[13] |
N. Lecocq, 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.
doi: doi:10.1017/S0022112004009942. |
[14] |
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 A, 5 (1993), 3-12.
doi: doi:10.1063/1.858787. |
[15] |
A. Lefebvre, Numerical simulation of gluey particles, M2AN Math. Model. Numer. Anal., 43 (2009), 53-80.
doi: doi:10.1051/m2an/2008042. |
[16] |
A. Lozinski and M. Romerio, Motion of gas bubbles, considered as massless bodies, affording deformations within a prescribed family of shapes, in an incompressible fluid under the action of gravitation and surface tension, M3AS Math. Mod. Meth. Appl. Sci., 17 (2007), 1445-1478.
doi: doi:10.1142/S0218202507002340. |
[17] |
A. A. Mammoli, The treatment of lubrication forces in boundary integral equations, Royal Society of London Proceedings Series A, 462 (2006), 855-881.
doi: doi:10.1098/rspa.2005.1600. |
[18] |
B. Maury, A gluey particle model, ESAIM: Proceedings, 18 (2007), 133-142.
doi: doi:10.1051/proc:071811. |
[19] |
M. O'Neill, A slow motion of viscous liquid caused by a slowly moving solid sphere, Mathematika, 11 (1964), 67-74. |
[20] |
M. O'Neill and K. Stewartson, On the slow motion of a sphere parallel to a nearby plane wall, J. Fluid Mech., 27 (1967), 705-724.
doi: doi:10.1017/S0022112067002551. |
[21] |
L. Pasol, M. Chaoui, S. Yahiaoui and F. Feuillebois, Analytical solutions for a spherical particle near a wall in axisymmetrical polynomial creeping flows, Phys. Fluids, 17 (2005), 1-13.
doi: doi:10.1063/1.1955272. |
[22] |
F. Qi, N. Phan-Tien and X. J. Fan, Effective moduli of particulate solids: The completed double layer boundary element method with lubrication approximation, Zeitschrift Angewandte Mathematik und Physik, 51 (2000), 92-113.
doi: doi:10.1007/PL00001509. |
[23] |
A. Sierou and J. F. Brady, Accelerated Stokesian dynamics simulations, Journal of Fluid Mechanics, 448 (2001), 115-146.
doi: doi:10.1017/S0022112001005912. |
[24] |
J. Smart and D. Leighton, Measurements of the hydrodynamic roughness of non colloidal spheres, Phys. Fluids A, 1 (1989), 52-60.
doi: doi:10.1063/1.857523. |
[25] |
O. Vinogradova and G. Yakubov, Surface roughness and hydrodynamic boundary conditions, Phys. Rev. E, 73 (2006), p. 045302(R).
doi: doi:10.1103/PhysRevE.73.045302. |
show all references
References:
[1] |
J. F. Brady and G. Bossis, Stokesian dynamics, Annual Review of Fluid Mechanics, 20 (1988), 111-157.
doi: oi:10.1146/annurev.fl.20.010188.000551. |
[2] |
J. Butcher, "Numerical Methods for Ordinary Differential Equations," John Wiley & Sons Ltd., Chichester, 2003.
doi: doi:10.1002/0470868279. |
[3] |
M. Cooley and M. O'Neill, On the slow motion generated in a viscous fluid by the approach of a sphere to a plane wall or stationary sphere, Mathematika, 16 (1969), 37-49.
doi: doi:10.1112/S0025579300004599. |
[4] |
S. L. Dance and M. R. Maxey, Incorporation of lubrication effects into the force-coupling method for particulate two-phase flow, Journal of Computational Physics, 189 (2003), 212-238.
doi: doi:10.1016/S0021-9991(03)00209-2. |
[5] |
W. R. Dean and M. E. O'Neill, A slow motion of viscous liquid caused by the rotation of a solid sphere, Mathematika, 10 (1963), 13-24.
doi: doi:10.1112/S0025579300003314. |
[6] |
G. P. Galdi, "An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Vol. I, Linearized Steady Problems," vol. 38 of Springer Tracts in Natural Philosophy, Springer-Verlag, New York, 1994. |
[7] |
D. Gérard-Varet and M. Hillairet, Regularity issues in the problem of fluid structure interaction, Arch. Ration. Mech. Anal., 195 (2010), 375-407.
doi: doi:10.1007/s00205-008-0202-9. |
[8] |
R. Glowinski, T.-W. Pan, T. I. Hesla and D. D. Joseph, A distributed lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiphase Flow, 24 (1999), 755-794.
doi: doi:10.1016/S0301-9322(98)00048-2. |
[9] |
F. Hecht, O. Pironneau, A. L. Hyaric and K. Ohtsuka, Freefem++, ver. 3.7, http://www.freefem.org/ff++, (2009). |
[10] |
M. Hillairet, Lack of collision between solid bodies in a 2D incompressible viscous flow, Comm. Partial Differential Equations, 32 (2007), 1345-1371.
doi: doi:10.1080/03605300601088740. |
[11] |
M. Hillairet and T. Takahashi, Collisions in three-dimensional fluid structure interaction problems, SIAM J. Math. Anal., 40 (2009), 2451-2477.
doi: doi:10.1137/080716074. |
[12] |
M. S. Ingber, A. Mammoli, P. Vorobieff, T. McCollam and A. Graham, Experimental and numerical analysis of irreversibilities among particles suspended in a couette device, Journal of Rheology, 50 (2006), 99-114.
doi: doi:10.1122/1.2169806. |
[13] |
N. Lecocq, 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.
doi: doi:10.1017/S0022112004009942. |
[14] |
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 A, 5 (1993), 3-12.
doi: doi:10.1063/1.858787. |
[15] |
A. Lefebvre, Numerical simulation of gluey particles, M2AN Math. Model. Numer. Anal., 43 (2009), 53-80.
doi: doi:10.1051/m2an/2008042. |
[16] |
A. Lozinski and M. Romerio, Motion of gas bubbles, considered as massless bodies, affording deformations within a prescribed family of shapes, in an incompressible fluid under the action of gravitation and surface tension, M3AS Math. Mod. Meth. Appl. Sci., 17 (2007), 1445-1478.
doi: doi:10.1142/S0218202507002340. |
[17] |
A. A. Mammoli, The treatment of lubrication forces in boundary integral equations, Royal Society of London Proceedings Series A, 462 (2006), 855-881.
doi: doi:10.1098/rspa.2005.1600. |
[18] |
B. Maury, A gluey particle model, ESAIM: Proceedings, 18 (2007), 133-142.
doi: doi:10.1051/proc:071811. |
[19] |
M. O'Neill, A slow motion of viscous liquid caused by a slowly moving solid sphere, Mathematika, 11 (1964), 67-74. |
[20] |
M. O'Neill and K. Stewartson, On the slow motion of a sphere parallel to a nearby plane wall, J. Fluid Mech., 27 (1967), 705-724.
doi: doi:10.1017/S0022112067002551. |
[21] |
L. Pasol, M. Chaoui, S. Yahiaoui and F. Feuillebois, Analytical solutions for a spherical particle near a wall in axisymmetrical polynomial creeping flows, Phys. Fluids, 17 (2005), 1-13.
doi: doi:10.1063/1.1955272. |
[22] |
F. Qi, N. Phan-Tien and X. J. Fan, Effective moduli of particulate solids: The completed double layer boundary element method with lubrication approximation, Zeitschrift Angewandte Mathematik und Physik, 51 (2000), 92-113.
doi: doi:10.1007/PL00001509. |
[23] |
A. Sierou and J. F. Brady, Accelerated Stokesian dynamics simulations, Journal of Fluid Mechanics, 448 (2001), 115-146.
doi: doi:10.1017/S0022112001005912. |
[24] |
J. Smart and D. Leighton, Measurements of the hydrodynamic roughness of non colloidal spheres, Phys. Fluids A, 1 (1989), 52-60.
doi: doi:10.1063/1.857523. |
[25] |
O. Vinogradova and G. Yakubov, Surface roughness and hydrodynamic boundary conditions, Phys. Rev. E, 73 (2006), p. 045302(R).
doi: doi:10.1103/PhysRevE.73.045302. |
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