SPH simulation of interacting solid bodies suspended in a shear flow of an Oldroyd-B fluid

Feng, 1996, Dynamic simulation of sedimentation of solid particles in an Oldroyd-B fluid, Journal of Non-Newtonian Fluid Mechanics, 63, 63, 10.1016/0377-0257(95)01412-8 Joseph, 1992, Competition between inertial pressures and normal stresses in the flow induced anisotropy of solid particles, 60 Huang, 1998, Direct simulation of the sedimentation of elliptic particles in Oldroyd-B fluids, Journal of Fluid Mechanics, 362, 297, 10.1017/S0022112098008672 Huang, 1997, Direct simulation of the motion of solid particles in Couette and Poiseuille flows of viscoelastic fluids, Journal of Fluid Mechanics, 343, 73, 10.1017/S0022112097005764 Ko, 2006, Lift and multiple equilibrium positions of a single particle in Newtonian and Oldroyd-B fluids, Computers & Fluids, 35, 121, 10.1016/j.compfluid.2004.12.001 Riddle, 1977, Interactions between two spheres falling along their line of centers in a viscoelastic fluid, Journal of Non-Newtonian Fluid Mechanics, 2, 23, 10.1016/0377-0257(77)80030-X Joseph, 1994, Aggregation and dispersion of spheres falling in viscoelastic liquids, Journal of Non-Newtonian Fluid Mechanics, 54, 45, 10.1016/0377-0257(94)80015-4 Singh, 2000, A distributed Lagrange multiplier/fictitious domain method for viscoelastic particulate flows, Journal of Non-Newtonian Fluid Mechanics, 91, 165, 10.1016/S0377-0257(99)00104-4 Hao, 2009, A fictitious domain/distributed Lagrange multiplier method for the particulate flow of Oldroyd-B fluids: a positive definiteness preserving approach, Journal of Non-Newtonian Fluid Mechanics, 156, 95, 10.1016/j.jnnfm.2008.07.006 Hwang, 2004, Direct simulations of particle suspensions in a viscoelastic fluid in sliding bi-periodic frames, Journal of Non-Newtonian Fluid Mechanics, 121, 15, 10.1016/j.jnnfm.2004.03.008 Choi, 2010, An extended finite element method for the simulation of particulate viscoelastic flows, Journal of Non-Newtonian Fluid Mechanics, 165, 607, 10.1016/j.jnnfm.2010.02.021 Yan, 2007, Hydrodynamic interaction of two particles in confined linear shear flow at finite Reynolds number, Physics of Fluids, 19, 113305, 10.1063/1.2786478 Rafiee, 2007, An incompressible SPH method for simulation of unsteady viscoelastic free-surface flows, International Journal of Non-Linear Mechanics, 42, 1210, 10.1016/j.ijnonlinmec.2007.09.006 Ellero, 2002, Viscoelastic flows studied by smoothed particle dynamics, Journal of Non-Newtonian Fluid Mechanics, 105, 35, 10.1016/S0377-0257(02)00059-9 Ellero, 2005, SPH simulations of transient viscoelastic flows at low Reynolds number, Journal of Non-Newtonian Fluid Mechanics, 132, 61, 10.1016/j.jnnfm.2005.08.012 Fang, 2006, A numerical study of the SPH method for simulating transient viscoelastic free surface flows, Journal of Non-Newtonian Fluid Mechanics, 139, 68, 10.1016/j.jnnfm.2006.07.004 R. Fatehi, M. Manzari, A consistent and fast weakly compressible smoothed particle hydrodynamics with a new wall boundary condition, International Journal for Numerical Methods in Fluids, doi:10.1002/fld.2586. Fatehi, 2011, Error estimation in smoothed particle hydrodynamics and a new scheme for second derivatives, Computers & Mathematics with Applications, 61, 482, 10.1016/j.camwa.2010.11.028 R. Fatehi, M. Manzari, A remedy for numerical oscillations in weakly compressible smoothed particle hydrodynamics, International Journal of Numerical Methods in Fluids, doi:10.1002/fld.2406. Monaghan, 1994, Simulating free surface flows with SPH, Journal of Computational Physics, 110, 399, 10.1006/jcph.1994.1034 Gingold, 1977, Smoothed particle hydrodynamics: theory and application to nonspherical stars, Astrophysical Journal, 181, 275 Randles, 1996, Smoothed particle hydrodynamics: some recent improvements and applications, Computer Methods in Applied Mechanics and Engineering, 139, 375, 10.1016/S0045-7825(96)01090-0 Bonet, 1999, Variational and momentum preservation aspects of smooth particle hydrodynamic formulations, Computer Methods in Applied Mechanics and Engineering, 180, 97, 10.1016/S0045-7825(99)00051-1 Vila, 1999, On particle weighted methods and smooth particle hydrodynamics, Mathematical Models and Methods in Applied Sciences, 9, 161, 10.1142/S0218202599000117 Lee, 2008, Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method, Journal of Computational Physics, 227, 8417, 10.1016/j.jcp.2008.06.005 Shao, 2003, Incompressible SPH method for simulating newtonian and non-newtonian flows with a free surface, Advances in Water Resources, 26, 787, 10.1016/S0309-1708(03)00030-7 Xu, 2009, Accuracy and stability in incompressible SPH (ISPH) based on the projection method and a new approach, Journal of Computational Physics, 228, 6703, 10.1016/j.jcp.2009.05.032 Wendland, 1995, Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree, Advances in Computational Mathematics, 4, 389, 10.1007/BF02123482 Morris, 1997, Modeling low Reynolds number incompressible flows using SPH, Journal of Computational Physics, 136, 214, 10.1006/jcph.1997.5776 Waters, 1970, Unsteady flow of an elastico-viscous liquid, Rheologica Acta, 9, 345, 10.1007/BF01975401 Hayat, 2004, Exact solutions of flow problems of an Oldroyd-B fluid, Applied Mathematics and Computation, 151, 105, 10.1016/S0096-3003(03)00326-6 Feng, 1994, Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2: Couette and Poiseuille flows, Journal of Fluid Mechanics, 277, 271, 10.1017/S0022112094002764