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

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We gratefully acknowledge the support of the NSF (grants ECCS-9527123, CBET-9873236, DMS-9973318, DMS-0209066, DMS-0443826, NSF DMS-0914788, NSF DMS-1418308) for developping the distributed Lagrange multiplier/fictitious domain methods for simulating particulate flows.

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Some 2D & 3D Results obtained by a distributed Lagrange multiplier/fictitious domain method with finite element method and operator splitting method:

• Particle Motion in Visco-elastic 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.
  1. Two balls form a verticl chain in a channel of square cross section: Elastic number E=5.
  2. Two balls separate in a channel of square cross section: Elastic number E=5.
• Animations of balls settling in a viscoelastic fluid of Oldroyd-B type ("Physics of Fluids" 30 (2018), 113102):
• Balls are released side-by-side initially (published in "Physics of Fluids" 30 (2018), 113102):
  1. 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.
  2. 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.
  3. Three balls form a 2-ball 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 side-by-side initial confoguration).
  4. Three balls form a 3-ball 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 side-by-side initial confoguration).
• Three Balls are released one atop the other initially (published in "Physics of Fluids" 30 (2018), 113102):
  1. Three balls form a 2-ball 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).
  2. Three balls form a 3-ball 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 Oldroyd-B fluid under creeping conditions (published in "Computers & Fluids" 172 (2018), 661-673):
1. Two balls pass over/under each other.
2. Two balls chain and tumble.
• Animations of settling disks in either Oldroyd-B or FENE-CR type viscoelastic fluid (published in "J. non-Newtonian Fluid Mech." 244 (2017), 44-56.):
1. Six disks form a long chain in a 2D channel filled with an Oldroyd-B fluid.
2. Six disks form two short chains in a 2D channel filled with a FENE-CR fluid for the polymer extension limit L=5.
3. Six disks form a long chain in a 2D channel filled with a FENE-CR fluid for L=200.
4. Ten disks settle in a 2D channel filled with a FENE-CR fluid for L=2: Stable chains of 2 disks are formed.
5. Ten disks settle in a 2D channel filled with a FENE-CR fluidf or L=5: Stable chains of 2 or 3 disks are formed.
6. Ten disks settle in a 2D channel filled with a FENE-CR fluid for L=200: Two stable chains of 4 disks are formed.
• Animations of an ellipsoid settling in a viscoelastic fluid of Oldroyd-B type:
1. 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), 410-425):
    (1) Pass over/under.
    (2) Return trajectories.
    (3) Two balls are close to each other initially (gap size 4h): pass over/under.
    (4) Two balls are close to each other initially (gap size 2h): tumbling.

  • Two neutrally buoyant prolate ellipsoids in a bounded shear flow under creeping conditions (published in "J. Comp. Phys." 352 (2018), 410-425):
    (1) Pass over/under.
    (2) Return trajectories.

  • Two and three balls settle in a narrow vertical channel (published in "Japan Journal of Industrial and Applied Mathematics" 25 (2008), 1-63):
    • Animations of two balls drafting, kissing and tumbling in a narrow vertical channel filled with an incompressible viscous Newtonian fluid:
      (1) Ball density=1.1,
      (2) Ball density=1.25.
    • Animations of three balls drafting, kissing and tumbling in a narrow vertical channel filled with an incompressible viscous Newtonian fluid:
      (1) Ball density=1.02,
      (2) Ball density=1.1,
      (3) Ball density=1.25.

  • 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
      • Three clusters are forming when the gap sizes between balls are about a quarter of the ball radius initially.
      • Four clusters are forming when the gap sizes between balls are about the ball radius initially.
    • 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.
      • Three clusters are forming for 0 < t< 30.
      • Three clusters are forming for 30 < t < 60.

  • Motion of Neutrally Buoyant Particles (published in "Comp. Meth. Appl. Mech. Eng." 197 (2008), 2198-2209):
    • Animation of the motion of a neutrally buoyant prolate ellipsoid with the long axis initially perpendicular to the cylinder axis in a tube filled with an incompressible viscous Newtonian fluid.
    • Animation of the motion of a neutrally buoyant prolate ellipsoid with the long axis initially parallel to the cylinder axis in a tube filled with an incompressible viscous Newtonian fluid.
    • Animation of the motion of a neutrally buoyant oblate ellipsoid in a tube filled with an incompressible viscous Newtonian fluid.
    • Animation of the motion of 120 neutrally buoyant ellipsoid in a tube filled with an incompressible viscous Newtonian fluid

  • Animations of settling ellipsoids in an incompressible viscous Newtonian fluid (Published in "Computers and Structures" 83 (2005), pp. 463-478):
  • Animation of a settling ellipsoid in a narrow vertical channel.
  • Animation of interaction of two ellipsoids sedimenting side-by-side in a narrow vertical channel.
  • Animation of interaction of two ellipsoids sedimenting in a narrow vertical channel.
  • Animations of settling cylinders in an incompressible viscous Newtonian fluid (Published in "J. Zhejiang Univ. SCI." 6A (2005), pp. 97--109):
  • Animation of a truncated cylinder settling in a narrow vertical channel.
  • Animation of interaction of two truncated cylinders settling in a narrow vertical channel.
  • Animation of fluidization of 60 truncated cylinders in a 2D like bed.
  • 1204 spheres fluidized bed (published in "J. Fluid Mech." 451 (2002), 169-191):
    • Case 1: U=3
    • Case 2: U=4
    • Case 3: U=4.5

  • Lifting of a particle:
    • Animation of a lifting of a ball in a horizontal pipe filled with an incompressible viscous Newtonian fluid
    • Animation of a lifting of a neutrally-buoyant ball in a horizontal pipe filled with an incompressible viscous Newtonian fluid
    • Animation of a lifting of an ellipsoid in a horizontal pipe ( side view ) filled with an incompressible viscous Newtonian fluid

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Research Funding

1. NSF DMS-1418308: Computational Mathematics (PI was T.-W. Pan, CO-PI was R. Glowinski).
   Grant title: Positive definiteness preserving approaches for viscoelastic flow of Oldroyd-B and FENE-CR types: Applications to particulate flow.
   Grant amount and duration: $234,212, 08/01/2014 - 07/30/2017.
2. NSF DMS-0914788: Computational Mathematics (the PI was T.-W. Pan, CO-PIs 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.
3. NSF DMS-0443826: NIGMS (the PI was S. Canic, and CO-PIs 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.
4. NSF DMS-0209066: Computational Mathematics (the PI was R. Glowinski, and CO-PIs 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.
5. NSF DMS-9973318: Computational Mathematics (the PI was R. Glowinski, and CO-PIs were T.-W. Pan, E. Dean and P.M. Pettitt).
   Grant title: Computational Methods for the Direct Simulation of Particulate Flow of Newtonian and Non-Newtonian Incompressible Viscous Fluids.
   Grant amount and duration: $171,000, 08/01/1999 - 07/31/2003.
6. NSF CBET-9873236: 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 Solid-Liquid Flows.
   Grant amount and duration: $337,388, 10/01/1998 – 09/30/2001;
7. NSF ECCS-9527123: HPCC Grand Challenge (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), 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.

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Publications

1. Ang Li, T.-W. Pan, and R. Glowinski
   On the DLM/FD methods for simulating neutrally buoyant swimmers moving in non-Newtonian shear thinning fluids
   International Journal for Numerical Methods in Fluids 94 (2022), 1465-1483.
   

2. 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.
   

3. T.-W. Pan, Shang-Huan Chiu and R. Glowinski
   Numerical study of two balls settling in viscoelastic fluids from an initial vertical configuration
   Physics of Fluids 31 (2019), 123104.
   

4. R. Glowinski and T.-W. Pan
   Two decades of wave-like 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. 221-250, Springer, Cham, 2019
   

5. T.-W. Pan and R. Glowinski
   Numerical study of spheres settling in Oldroyd-B fluids
   Physics of Fluids 30 (2018), 113102.
   

6. Liang-Hsia Tsai, Chien-Cheng Chang, T.-W. Pan, R. Glowinski
   Numerical study of the wall effect on particle sedimentation
   International Journal of Computational Fluid Dynamics 32 (2018), 158-166.
   

7. Shang-Huan Chiu, T.-W. Pan, R. Glowinski
   A 3D DLM/FD method for simulating the motion of spheres in a bounded shear flow of Oldroyd-B fluids
   Computers & Fluids 172 (2018), 661-673; arXiv:1707.01957.
   

8. 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), 535-552.
   

9. T.-W. Pan, Aixia Guo, Shang-Huan 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), 410-425.
   

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

11. 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), 397-412.
    

12. T.-W. Pan, R. Glowinski
    Dynamics of particle sedimentation in viscoelastic fluids: A numerical study on particle chain in two-dimensional narrow channel
    Journal of Non-Newtonian Fluid Mechanics 244 (2017), 44-56.
    

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

14. Shih-Lin Huang, Shih-Di Chen, T.-W. Pan, Chien-Cheng Chang, Chin-Chou 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.
    

15. 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), 241-253.
    

16. Che-Ming Shih, Chun-Fei Kung, Chien-Cheng Chang and T.-W. Pan
    Self-organized capacity for energy extraction by clustering particles in two-species suspension flow at small Reynolds numbers
    Applied Physics Letters 106 (2015), 024102.
    

17. 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.
    

18. Suchung Hou, T.-W. Pan, R. Glowinski
    Circular band formation for incompressible viscous fluid-rigid particle mixtures in a rotating cylinder
    Physical Review E 89 (2014), 023013.
    

19. T.-W. Pan, Shih-Lin Huang, Shih-Di Chen, Chin-Chou Chu, Chien-Cheng Chang
    A numerical study of the motion of a neutrally buoyant cylinder in two dimensional shear flow
    Computers & Fluids 87 (2013), 57-66.
    

20. Shih-Di Chen, T-W Pan, Chien-Cheng Chang
    The motion of a single and multiple neutrally buoyant elliptical cylinders in plane Poiseuille flow
    Physics of Fluids 24 (2012), 103302.
    

21. 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), 975-990.
    

22. Jian Hao, T.-W. Pan, S. Canic, R. Glowinski, D. Rosenstrauch
    A fluid-cell interaction and adhesion algorithm for tissue-coating of cardiovascular implants
    SIAM Journal on Multiscale Modeling and Simulation 7 (2009), 1669-1694.
    

23. Jian Hao, T.-W. Pan, R. Glowinski, D.D. Joseph
    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 (2009), 95-111.
    

24. T.-W. Pan, C.-C. Chang, R. Glowinski
    On the motion of a neutrally buoyant ellipsoid in a three-dimensional Poiseuille flow
    Computer Methods in Applied Mechanics and Engineering 197 (2008), 2198-2209.
    

25. R. Glowinski, E. Dean, G. Guidoboni, L.H. Juarez V., T.-W. Pan
    Operator-splitting methods for the numerical simulation of particulate and
    free-surface flows and for the numerical solution of elliptic Monge-Ampere equation
    Japan Journal of Industrial and Applied Mathematics 25 (2008), 1-63.
    

26. T.-W. Pan, R. Glowinski, Suchung Hou
    Direct numerical simulation of pattern formation in a rotating suspension
    of non-Brownian settling particles in a fully filled cylinder
    Computers & Structures 85 (2007), 955-969.
    

27. R. Glowinski, T.-W. Pan, J. Periaux
    Numerical simulation of a multi-store separation phenomenon: A fictitious domain approach
    Computer Methods in Applied Mechanics and Engineering 195 (2006), 5566-5581.
    

28. T.-W. Pan, R. Glowinski, D.D. Joseph
    Simulating the dynamics of fluid-cylinder interactions
    Journal of Zhejiang University Science 6A (2005), 97-109.
    

29. T.-W. Pan, R. Glowinski, D.D. Joseph
    Simulating the dynamics of fluid-ellipsoid interactions
    Computers and Structures 83 (2005), 463-478.
    

30. 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), 109-131.
    

31. T.-W. Pan, R. Glowinski
    Direct simulation of the motion of neutrally buoyant balls in a three-dimensional Poiseuille flow
    C. R. Mecanique, Acad. Sci. Paris 333 (2005), 884-895.
    

32. 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), 49-102.
    

33. 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), 169-191.
    

34. 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 Taylor-Hood finite element approximation
    Journal of Scientific Computing 17 (2002), 683-694.
    

35. 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), 260-279.
    

36. 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), 71-82.
    

37. T.-W. Pan, D.D. Joseph, R. Glowinski
    Modeling Rayleigh-Taylor instability of a sedimenting suspension of several
    thousand circular particles in direct numerical simulation
    Journal of Fluid Mechanics 434 (2001), 23-37.
    

38. 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), 363-427.
    

39. 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), 435-438.
    

40. 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), 1509-1524.
    

41. 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. Non-Newtonian Fluid Mech. 91 (2000), 165-188.
    

42. 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), 241-268.
    

43. 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., North-Holland, Amsterdam, 2000, 329-336.
    

44. 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), 1035-1038.
    

45. 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), 1043-1066.
    

46. 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), 755-794.
    

47. 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), 181-194.
    

48. J. Feng, D. D. Joseph, R. Glowinski, T.-W. Pan
    A three-dimensional computation on the force and moment
    on an ellipsoid settling slowly through a viscoelastic fluid
    Journal of Fluid Mechanics 283 (1995), 1-16.