Rationale

Problems of bio-fluid or fluid mechanics often involve an interaction of a viscous incompressible fluid with an elastic/rigid moving structure. The immersed boundary (IB) method was first introduced by Charlie Peskin in 1972 to simulate the blood flow interacting with the valve leaflet in the heart. The remarkable feature of the method is that the entire simulation was carried out on a Cartesian grid despite the complex geometry of embedding structure. A novel forcing procedure was formulated to impose the effect of the immersed boundary. The fluid and the structure are linked by a smoothed version of Dirac delta function. Although the method is firstly designed for the fluid flows with elastic structures, the method has become more and more popular for the simulation of fluid flows interacting with complex rigid boundary. Since the introduction of this method, numerous variants of approaches and applications have been proposed and the method continues to be a promising tool for the researchers in the bio-fluid and fluid mechanics community.

As mentioned above, the interaction between the fluid and the immersed boundary are linked by the discrete delta function which degrades the overall accuracy of the method. So in contrast to the discrete delta function approach, the immersed interface method (IIM) was invented by Randy LeVeque and Zhilin Li to incorporates the jump conditions into finite difference scheme for the elliptic problems with interfaces. Thus, the method has improved the accuracy and can obtain sharp interface solutions. By employing the level set method for the representation of the interface, the IIM has been also applied to different problems such as Stefan and crystal growth problems, Stokes or Navier-Stokes flows with surface tension, and insect flight problems. Recently, the IIM has also been applied to the fluid problems in irregular domains.

The main theme of this mini symposium is to bring the above two groups of people together and to demonstrate the current possible applications of those methods. It will be a nice section for researchers interested in bio fluid mechanical simulation to exchange ideas and to initiate possible collaborations.

Program