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

• 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.
• Two and three balls settling in a narrow vertical channel (published in "Japan Journal of Industrial and Applied Mathematics" 25 (2008), 1-63):
  • Animation of two balls settling in a narrow vertical channel filled with an incompressible viscous Newtonian fluid:
    (1) Ball density=1.1,
    (2) Ball density=1.25.
  • Animation of three balls settling in a narrow vertical channel filled with an ncompressible 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 "Computers and Structures" 85 (2007), pp. 955-969):
  • Animations of pattern formation in a rotating suspension of 80 settling balls in a horizontal cylinder in an incompressible viscous Newtonian fluid with angular speed equal to 8:
    • 10 < t < 20: three clusters are forming.
    • 40 < t < 50: three clusters
  • Animations of pattern formation in a rotating suspension of 160 settling balls in a longer horizontal cylinder in an incompressible viscous Newtonian fluid:
    • Angular velocity = 8: 10 < t < 30, six clusters are forming.
    • Angular velocity = 8: 65 < t < 75, six clusters are forming.
    • Angular velocity = 12: 65 < t < 75, some clusters are forming (with same initial conditions as the case of angular speed equal to 8).

• 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

• 1204 balls 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 an ellipsoid in a horizontal pipe ( side view ) filled with an incompressible viscous Newtonian fluid

• Animations of a settling ellipsoid in an visco-elastic fluid of Oldroyd-B type
• Case 1: Ellipsoid turns its broadside parallel to the stream in a channel of square cross section: Particle Reynolds Number Re < 1 and Mach number M < 1
• Case 2: Ellipsoid turns its broadside parallel to the stream in a channel of rectangular cross section: Particle Reynolds Number Re < 1 and Mach number M < 1
• Case 3: Ellipsoid turns its broadside parallel to the stream in a channel of rectangular cross section: Particle Reynolds Number Re = O(1) and Mach number M = O(1)