Efficient Immersed Boundary Method for Strong Interaction Problem of Arbitrary Shape Object with the Self-Induced Flow

An immersed boundary method is improved and applied to 2-D flow fields involving a single stationary/moving object. The present immersed boundary method employs a body force proportional to a solid volume fraction for coupling the solid and fluid motions at the interface. A hyperbolic-tangent function is newly introduced as a surface digitiser for computing the volume fractions at the interface cells, and this improvement is proved to be efficient for problems involving arbitrary shape object. The present method is applied to a uniform flow field around a circular cylinder and an interaction problem of fluid and free-falling object. The computational results are found to agree with the results by the different methods of the present authors and the results reported in the literatures. Also the computation time is considerably cut down compared to the other methods by the series of improvements to the immersed boundary method.

[1]  C. Peskin.  Flow patterns around heart valves: A numerical method , 1972 .

[2]  R. Henderson.  Details of the drag curve near the onset of vortex shedding , 1995 .

[3]  B. R. Noack,et al.  On the transition of the cylinder wake , 1995 .

[4]  L. K. Taylor,et al.  Strong Conservative Form of the Incompressible Navier—Stokes Equations in a Rotating Frame with a Solution Procedure , 1996 .

[5]  C. Williamson.  Vortex Dynamics in the Cylinder Wake , 1996 .

[6]  C. W. Hirt,et al.  An Arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds , 1997 .

[7]  A. Popel,et al.  Large deformation of red blood cell ghosts in a simple shear flow. , 1998, Physics of fluids.

[8]  On the numerical simulation of round jets of incompressible fluid , 1999 .

[9]  T. Kajishima,et al.  Turbulence Structure of Particle-Laden Flow in a Vertical Plane Channel Due to Vortex Shedding , 2001 .

[10]  T. Kajishima,et al.  Interaction between particle clusters and particle-induced turbulence , 2002 .

[11]  Akihiko Shimizu,et al.  Unsteady three-dimensional simulation of interactions between flow and two particles , 2003 .

[12]  Difference Formula of Poisson Equation Consistent with an Immersed Boundary Method , 2004 .

[13]  Shintaro Takeuchi,et al.  Discrete element simulation of a flat-bottomed spouted bed in the 3-D cylindrical coordinate system , 2004 .

[14]  Study of Solid-Fluid Interaction in Body-Fixed Non-Inertial Frame of Reference , 2006 .

[15]  Haecheon Choi,et al.  Immersed boundary method for flow around an arbitrarily moving body , 2006, J. Comput. Phys..