The Immersed Boundary(IB) Method :

  • The IB method is a generally useful method for problems in which elastic materials interact with a viscous incompressible fluid. In the IB formulation, the influence of the elastic material immersed in the fluid appears as a localized body force acting on the fluid. This body force arises from the elastic stresses of the material. Moreover, the immersed material is required to move at the local fluid velocity as a consequence of the no-slip condition. This whole approach has been applied successfully to problems of blood flow in the heart, wave propagation in the cochlea, platelet aggregation during blood clotting and several other problems.

  • The penalty IB method which was introduced by C.S.Peskin and myself is a new and simple way to give mass to the elastic boundary within the IB framework. The key idea is to introduce a massive boundary point as a twin of each immersed boundary marker where mass is needed. The two boundaries are supposed to be the same, and when they move apart, a strong restoring force arises to pull them back together. The massive boundary moves according to Newton's law without interacting directly with the fluid, and the original immersed boundary plays the same role as in the original IB method with no mass.

  • 3-D Parachute Simulation

    Let a parachute with a massive payload fall freely and make wind blow up to prevent the parachute from going out of the domain. Then we can simulate many different situations below: dropping parachute onto the ground, inflation of almost closed parachute, one parachute with vortex, interaction of two parachutes. The red dots show the trails of some fluid makers.

    Dropping parachute
    Parachute opening
    One parachute
    Cluster parachute
    Two parachutes

  • a flapping filament in a soap film
    ( figure): a filament is flapping with mass (right) and not flapping without mass (left).
    -a windsock in winds of different speeds, and a flapping and sagging flag.

  • Papers in Preparation:
    - Penalty Immersed Boundary Method for an Elastic Boundary with Mass.(.pdf)
    Physics of Fluids, 2007.(with C.S.Peskin)
    - On Various Techniques for Computer Simulation of Boundaries with Mass.(.pdf)
    2nd MIT conference on Solid and Fluid Mechanics.(with L.Zhu, X.Wang, and C.S.Peskin)
    - 2-D Parachute Simulation by the Immersed Boundary Method.(.pdf)
    SIAM Journal on Scientific Computing, 2006.(with C.S.Peskin)
    - 3-D Parachute Simulation by the Immersed Boundary Method.(.pdf)
    Computers and Fluids, 2009.(with C.S.Peskin)

  • Papers in Preparation:
    - 3-D Flag Simulations by the Penalty Immersed Boundary Method.(.pdf)
    to be submitted.(with C.S.Peskin)
    - High Order Poisson solver with Complicated geometry and a Singular Source(.pdf)
    to be submitted.