
Fluid/Particle interaction
Particulate Flow Research Group
Department of Mathematics
University of Houston
Houston, TX 77204


We gratefully acknowledge the support of the NSF (grants ECCS9527123, CBET9873236, DMS9973318, DMS0209066, DMS0443826, NSF DMS0914788, NSF DMS1418308)
for developping
the distributed Lagrange multiplier/fictitious domain methods for simulating particulate flows.
Some 2D & 3D Results obtained by a distributed Lagrange multiplier/fictitious domain method
with finite element method and operator splitting method:
 Particle Motion in Viscoelastic Fluids:
 Two Balls are released one atop the other initially (published in "Physics of Fluids" 31 (2019), 123104):
The ball density, initial gap between two balls, and fluid elasticity number matter for the separation of the two balls.
 Two balls form a verticl chain in a channel of square cross section: Elastic number E=5.
 Two balls separate in a channel of square cross section: Elastic number E=5.
 Animations of balls settling in a viscoelastic fluid of OldroydB type ("Physics of Fluids" 30 (2018), 113102):
 Balls are released sidebyside initially (published in "Physics of Fluids" 30 (2018), 113102):
 Two balls form a verticl chain in a channel of square cross section: Elastic number E=1, Particle Reynolds Number < 1 and Mach number < 1.
 Two balls form a verticl chain in a channel of square cross section: Elastic number E=2, Particle Reynolds Number < 1 and Mach number < 1.
 Three balls form a 2ball verticl chain in a channel of square cross section: Elasticity number E=4, Particle Reynolds Number < 1 and Mach number < 1 (the density of balls = 1.12 with a sidebyside initial confoguration).
 Three balls form a 3ball verticl chain in a channel of square cross section: Elasticity number E=4, Particle Reynolds Number < 1 and Mach number < 1 (the density of balls = 1.13 with a sidebyside initial confoguration).
 Three Balls are released one atop the other initially (published in "Physics of Fluids" 30 (2018), 113102):
 Three balls form a 2ball verticl chain in a channel of square cross section: Elasticity number E=4, Particle Reynolds Number < 1 and Mach number < 1 (the density of balls = 1.14 with a vertical initial confoguration).
 Three balls form a 3ball verticl chain in a channel of square cross section: Elasticity number E=4, Particle Reynolds Number < 1 and Mach number < 1 (the density of balls = 1.15 with a vertical initial confoguration).
 Animations of two neutrally buoyant balls interacting in a bounded shear flow of an OldroydB fluid under creeping conditions (published in "Computers & Fluids" 172 (2018), 661673):
 Two balls pass over/under each other.
 Two balls chain and tumble.
 Animations of settling disks in either OldroydB or FENECR type viscoelastic fluid (published in "J. nonNewtonian Fluid Mech." 244 (2017), 4456.):
 Six disks form a long chain in a 2D channel filled with an OldroydB fluid.
 Six disks form two short chains in a 2D channel filled with a FENECR fluid for the polymer extension limit L=5.
 Six disks form a long chain in a 2D channel filled with a FENECR fluid for L=200.
 Ten disks settle in a 2D channel filled with a FENECR fluid for L=2: Stable chains of 2 disks are formed.
 Ten disks settle in a 2D channel filled with a FENECR fluidf or L=5: Stable chains of 2 or 3 disks are formed.
 Ten disks settle in a 2D channel filled with a FENECR fluid for L=200: Two stable chains of 4 disks are formed.
 Animations of an ellipsoid settling in a viscoelastic fluid of OldroydB type:
 An ellipsoid turns its broadside parallel to the stream in a channel of square cross section: Particle Reynolds Number < 1 and Mach number < 1
 Particle Motion in Newtonian Fluids:

Two neutrally buoyant balls in a bounded shear flow under creeping conditions (published in "J. Comp. Phys." 352 (2018), 410425):

Two neutrally buoyant prolate ellipsoids in a bounded shear flow under creeping conditions (published in "J. Comp. Phys." 352 (2018), 410425):

Two and three balls settle in a narrow vertical channel (published in "Japan Journal of Industrial and Applied Mathematics" 25 (2008), 163):

Pattern formation in a fully filled rotating cylinder (published in "Physical Review E 89 (2014), 023013"):

Animations of a
pattern formation in a rotating suspension of 192 settling
balls in an incompressible viscous Newtonian
fluid in a truncated cylinder horizontally rotating with angular speed of 12: the effect of the gap size between balls

Animations of a pattern formation in a rotating suspension of 128 settling
balls in an incompressible viscous Newtonian
fluid in a truncated cylinder horizontally rotating at the angular speed of 12: Sedimentating first
and then rotating.
 Motion of Neutrally Buoyant Particles (published in "Comp. Meth. Appl. Mech. Eng." 197 (2008), 21982209):

Animations of settling ellipsoids in an
incompressible viscous Newtonian fluid (Published in "Computers and Structures"
83 (2005), pp. 463478):

Animations of settling cylinders in an
incompressible viscous Newtonian fluid (Published in "J. Zhejiang Univ. SCI."
6A (2005), pp. 97109):
 1204 spheres fluidized bed (published in "J. Fluid Mech." 451 (2002), 169191):
 Lifting of a particle:
Research Funding
 NSF DMS1418308: Computational Mathematics (PI was T.W. Pan, COPI was
R. Glowinski).
Grant title: Positive definiteness preserving approaches for viscoelastic flow of OldroydB and FENECR types:
Applications to particulate flow.
Grant amount and duration: $234,212, 08/01/2014  07/30/2017.
 NSF DMS0914788: Computational Mathematics (the PI was T.W. Pan, COPIs were
R. Glowinski and R. Hoppe).
Grant title: Computational methods for the suspensions of deformable and rigid particles
and their applications to modelling of blood flows.
Grant amount and duration: $340,454, 07/15/2009  07/30/2014.
 NSF DMS0443826: NIGMS (the PI was S. Canic, and COPIs were R. Glowinski
and T.W. Pan).
Grant title: Collaborative research: Modeling the growth and adhesion of auricular
chondrocytes under controlled flow conditions.
Grant amount and duration: $740,000, 05/15/2005  04/30/2010.
 NSF DMS0209066: Computational Mathematics (the PI was R. Glowinski,
and COPIs were T.W. Pan and E. Dean).
Grant title: Numerical Simulation of Complex Incompressible Viscous Flow in Time Varying Geometries: Applications.
Grant amount and duration: $368,802, 07/01/2002  06/30/2006.
 NSF DMS9973318: Computational Mathematics (the PI was R. Glowinski, and
COPIs were T.W. Pan, E. Dean and P.M. Pettitt).
Grant title: Computational Methods for the Direct Simulation of Particulate Flow of
Newtonian and NonNewtonian Incompressible Viscous Fluids.
Grant amount and duration: $171,000, 08/01/1999  07/31/2003.
 NSF CBET9873236: KDI/NCC (with R. Glowinski and supported as a senior researcher),
the PI was D.D. Joseph (U. of Minnesota) and CO–PIs were R. Glowinski (U.of
Houston), H.H. Hu (U. of Pennsylvania), Y. Saad (U. of Minnesota) and A. Sameh (Purdue).
Grant title: KDI: Direct Numerical Simulation and Modeling of SolidLiquid Flows.
Grant amount and duration: $337,388, 10/01/1998 – 09/30/2001;
 NSF ECCS9527123: HPCC Grand Challenge (with R. Glowinski and supported as a senior
researcher), the PI was D.D. Joseph (U. of Minnesota) and COPIs were R. Glowinski (U.of
Houston), G. Golub (Stanford), H.H. Hu (U. of Pennsylvania), and A. Sameh (U. of Minnesota).
Grant title: MDC: Direct Simulation of the Motion of Particles in Flowing Liquids.
Grant amount and duration: $389,400, 10/01/1995 – 09/30/1998.
Publications
 Ang Li, T.W. Pan, and R. Glowinski
On the DLM/FD methods for simulating neutrally buoyant swimmers moving in nonNewtonian shear thinning fluids
International Journal for Numerical Methods in Fluids 94 (2022), 14651483.
 T.W. Pan, Ang Li and R. Glowinski
Numerical study of equilibrium radial positions of neutrally buoyant balls in circular Poiseuille flows
Physics of Fluids 33 (2021), 033301.
 T.W. Pan, ShangHuan Chiu and R. Glowinski
Numerical study of two balls settling in viscoelastic fluids from an initial vertical configuration
Physics of Fluids 31 (2019), 123104.
 R. Glowinski and T.W. Pan
Two decades of wavelike equation for numerical simulating of incompressible viscous flow: a review
In "Contributions to Partial Differential Equations and Applications" (Chetverushkin et al. eds.),
Computational Methods in Applied Sciences, vol 47, pp. 221250, Springer, Cham, 2019
 T.W. Pan and R. Glowinski
Numerical study of spheres settling in OldroydB fluids
Physics of Fluids 30 (2018), 113102.

LiangHsia Tsai, ChienCheng Chang, T.W. Pan, R. Glowinski
Numerical study of the wall effect on particle sedimentation
International Journal of Computational Fluid Dynamics 32 (2018), 158166.

ShangHuan Chiu, T.W. Pan, R. Glowinski
A 3D DLM/FD method for simulating the motion of spheres in a bounded shear flow of OldroydB fluids
Computers & Fluids 172 (2018), 661673; arXiv:1707.01957.
 Shihai Zhao, Yao Yu, T.W. Pan, R. Glowinski
A DLM/FD/IB method for simulating compound cell Interacting with red blood cells in a microchannel
Chinese Annals of Mathematics, Series B 39 (2018), 535552.

T.W. Pan, Aixia Guo, ShangHuan Chiu, R. Glowinski
A 3D DLM/FD method for simulating the motion of spheres and ellipsoids under creeping flow conditions
J. Comput. Phys. 352 (2018), 410425.

T.W. Pan, R. Glowinski
Dynamics of two disks settling in a twodimensional narrow channel: From periodic motion to vertical chain in OldroydB fluid
Physical Review E96, 063103 (2017); arXiv preprint (2016)
arXiv:1607.06009

Aixia Guo, T.W. Pan, Jiwen He, R. Glowinski
Numerical methods for simulating the motion of porous balls in simple 3D shear flows under creeping conditions
Computational Methods in Applied Mathematics
17 (2017), 397412.

T.W. Pan, R. Glowinski
Dynamics of particle sedimentation in viscoelastic fluids: A numerical study on particle chain in twodimensional narrow channel
Journal of NonNewtonian Fluid Mechanics
244 (2017), 4456.

T.W. Pan, R. Glowinski
Dynamics of two disks settling in a twodimensional narrow channel: From periodic motion to vertical chain in OldroydB fluid
arXiv preprint (2016)
arXiv:1607.06009

ShihLin Huang, ShihDi Chen, T.W. Pan, ChienCheng Chang, ChinChou Chu
The motion of a neutrally buoyant particle of an elliptic shape in two
dimensional shear flow: a numerical study
Physics of Fluids 27 (2015), 083303.

T.W. Pan, Shihai Zhao, Xiting Niu, R. Glowinski
A DLM/FD/IB method for simulating compound vesicle motion under creeping flow condition
J. Comput. Phys. 300 (2015), 241253.

CheMing Shih, ChunFei Kung, ChienCheng Chang and T.W. Pan
Selforganized capacity for energy extraction by clustering particles
in twospecies suspension flow at small Reynolds numbers
Applied Physics Letters 106 (2015), 024102.
 Lingling Shi, Yao Yu, T.W. Pan, R. Glowinski
Oscillating motions of neutrally buoyant particle and red blood
cell in Poiseuille flow in a narrow channel
Physics of Fluids 26 (2014) 041904.
 Suchung Hou, T.W. Pan, R. Glowinski
Circular band formation for incompressible viscous fluidrigid
particle mixtures in a rotating cylinder
Physical Review E 89 (2014), 023013.
 T.W. Pan, ShihLin Huang, ShihDi Chen, ChinChou Chu, ChienCheng Chang
A numerical study of the motion of a neutrally buoyant cylinder in two dimensional shear flow
Computers & Fluids 87 (2013), 5766.
 ShihDi Chen, TW Pan, ChienCheng Chang
The motion of a single and multiple neutrally buoyant elliptical cylinders in plane Poiseuille flow
Physics of Fluids 24 (2012), 103302.
 T.W. Pan, L. Shi, R. Glowinski
A DLM/FD/IB method for simulating cell/cell and cell/ particle interaction in microchannels
Chin. Annal Math., Ser. B 31(2010), 975990.
 Jian Hao, T.W. Pan, S. Canic, R. Glowinski, D. Rosenstrauch
A fluidcell interaction and adhesion algorithm
for tissuecoating of cardiovascular implants
SIAM Journal on Multiscale Modeling and Simulation 7 (2009), 16691694.
 Jian Hao, T.W. Pan, R. Glowinski, D.D. Joseph
A fictitious domain/distributed Lagrange multiplier method for the particulate
flow of OldroydB fluids: A positive definiteness preserving approach
Journal of NonNewtonian Fluid Mechanics 156 (2009), 95111.
 T.W. Pan, C.C. Chang, R. Glowinski
On the motion of a neutrally buoyant ellipsoid in a threedimensional Poiseuille flow
Computer Methods in Applied Mechanics and Engineering 197 (2008), 21982209.
 R. Glowinski, E. Dean, G. Guidoboni, L.H. Juarez V., T.W. Pan
Operatorsplitting methods for the numerical simulation of particulate and
freesurface flows and for the numerical solution of elliptic MongeAmpere equation
Japan Journal of Industrial and Applied Mathematics 25 (2008), 163.
 T.W. Pan, R. Glowinski, Suchung Hou
Direct numerical simulation of pattern formation in a rotating suspension
of nonBrownian settling particles in a fully filled cylinder
Computers & Structures 85 (2007), 955969.
 R. Glowinski, T.W. Pan, J. Periaux
Numerical simulation of a multistore separation phenomenon: A fictitious domain approach
Computer Methods in Applied Mechanics and Engineering 195 (2006), 55665581.

T.W. Pan, R. Glowinski, D.D. Joseph
Simulating the dynamics of fluidcylinder interactions
Journal of Zhejiang University Science 6A (2005), 97109.
 T.W. Pan, R. Glowinski, D.D. Joseph
Simulating the dynamics of fluidellipsoid interactions
Computers and Structures 83 (2005), 463478.
 B.H. Yang, J. Wang, D.D. Joseph, H.H. Hu, T.W. Pan, R. Glowinski
Numerical study of particle migration in tube and plane Poiseuille flows
Journal of Fluid Mechanics 540 (2005), 109131.
 T.W. Pan, R. Glowinski
Direct simulation of the motion of neutrally buoyant balls in a threedimensional Poiseuille flow
C. R. Mecanique, Acad. Sci. Paris 333 (2005), 884895.
 L.H. Juarez, R. Glowinski, T.W. Pan
Numerical simulation of fluid flow with moving and free boundaries
Boletin de la Sociedad Espanola de Matematica Aplicada 30 (2004), 49102.
 T.W. Pan, D.D. Joseph, R. Bai, R. Glowinski, V. Sarin
Fluidization of 1204 spheres: simulation and experiments
Journal of Fluid Mechanics 451 (2002), 169191.
 L.H. Juarez, R. Glowinski, T.W. Pan
Numerical simulation of the sedimentation of rigid bodies in an incompressible viscous fluid
by Lagrange multiplier/fictitious domain methods combined
with the TaylorHood finite element approximation
Journal of Scientific Computing 17 (2002), 683694.
 T.W. Pan, R. Glowinski
Direct simulation of the motion of neutrally buoyant circular cylinders in plane Poiseuille flow
Journal of Computational Physics 181 (2002), 260279.
 T.W. Pan, R. Glowinski, G.P. Galdi
Direct simulation of the motion of a settling ellipsoid in Newtonian fluid
Journal of Computational and Applied Mathematics 149 (2002), 7182.
 T.W. Pan, D.D. Joseph, R. Glowinski
Modeling RayleighTaylor instability of a sedimenting suspension of several
thousand circular particles in direct numerical simulation
Journal of Fluid Mechanics 434 (2001), 2337.
 R. Glowinski, T.W. Pan, T. I. Hesla, D. D. Joseph, J. Periaux
A fictitious domain approach to the direct numerical simulation of
incompressible viscous flow past moving rigid bodies: Application to particulate flow
Journal of Computational Physics 169 (2001), 363427.
 T.W. Pan
Numerical simulation of the motion of neutrally buoyant particles
in plane Poiseuille flow of a Newtonian fluid
C. R. Acad. Sci. Paris, Serie IIb 329 (2001), 435438.
 N. A. Patankar, P. Singh, D. D. Joseph, R. Glowinski, T.W. Pan
A new formulation of the distributed Lagrange multiplier/fictitious
domain method for particulate flows
Int. J. Multiphase Flow 26 (2000), 15091524.
 P. Singh, D. D. Joseph, T. I. Hesla, R. Glowinski, T.W. Pan
A distributed Lagrange multiplier/fictitious domain method for
viscoelastic particulate flows
J. NonNewtonian Fluid Mech. 91 (2000), 165188.
 R. Glowinski, T.W. Pan, T. I. Hesla, D. D. Joseph, J. Periaux
A distributed Lagrange multiplier/fictitious domain method for
the simulation of flows around moving rigid bodies: Application to particulate flow
Computer Methods in Applied Mechanics and Engineering 184 (2000), 241268.
 T.W. Pan, V. Sarin, R. Glowinski, J. Periaux, A. Sameh
Parallel solution of multibody store separation by a fictitious domain method
in Parallel CFD '99, D. Keyes ed., NorthHolland, Amsterdam, 2000, 329336.
 T.W. Pan
Numerical simulation of the motion of a ball falling in an incompressible viscous fluid
C. R. Acad. Sci. Paris , Serie IIb 327 (1999), 10351038.
 R. Glowinski, T.W. Pan, T. I. Hesla, D. D. Joseph, J. Periaux
A distributed Lagrange multiplier/fictitious domain method for flows
around moving rigid bodies: Application to particulate flow
International Journal for Numerical Methods in Fluids 30 (1999), 10431066.
 R. Glowinski, T.W. Pan, T. I. Hesla, D.D. Joseph
A distributed Lagrange multiplier/fictitious domain method for particulate flows
International Journal of Multiphase Flow 25 (1999), 755794.
 R. Glowinski, T.W. Pan, J. Periaux
Distributed Lagrange multiplier methods for incompressible
viscous flow around moving rigid bodies
Comp. Meth. Appl. Mech. Eng. 151 (1998), 181194.
 J. Feng, D. D. Joseph, R. Glowinski, T.W. Pan
A threedimensional computation on the force and moment
on an ellipsoid settling slowly through a viscoelastic fluid
Journal of Fluid Mechanics 283 (1995), 116.