Below is based upon my graduate research at the California Institute of Technology. I am currently a postdoctoral research associate at Princeton University. My current research projects involve (1) modeling and control of plasma in NSTX and (2) the development of the accelerated 3D parallel immersed boundary projection method computer code for simulating incompressible flows over moving bodies. More on these are to be available soon.

My research involves a new formulation of the immersed boundary method to simulate incompressible flow over bodies that can have complex geometries, be in motion, or be under deformation [1, 2, see below]. We use this method to perform numerical simulations of flow over low-aspect-ratio wings at very low Reynolds numbers. This analysis is intended to aid the development of micro-air-vehicles and their control laws [3, 4, 5].

Information on my research can also be found on Prof Colonius' wiki page.

My list of publications can be found in my CV: pdf format.

Figure 1: wake behind a translating flat rectangular plate (AR = 2, Re=300, AoA=30deg)

Immersed Boundary Projection Method

We are interested in simulating incompressible flow over moving/deforming bodies. To simulate such flow, we use a method called the immersed boundary projection method [1]. Similar to previous immersed boundary methods, boundary force is applied along the immersed boundary to satisfy the no-slip condition. In the present method, this force is treated in an analogous manner to pressure since both variables act as Lagrange mutipliers to satisfy kinematic constrains imposed on the flow, namely the no-slip and divergence-free constraints, respectively. Combining these two variables together allows us to formulate the immersed boundary method in an algebraically identical structure with the traditional fractional step methods. Some highlights of this method are:

- moving and stationary body simulation

- no-constitutive relation required for force calculation

- preservation of symmetry and positive definiteness

- no-slip enforced by projection

- max CFL = 1

This method can be accelerated by using a nullspace approach to satisfy the incompressibility constraint. The resulting system of equations can then be solved efficiently with the use of FFT in the case of a uniform Cartesian grid. In the far-field, a multi-domain approach is taken to account for the potential flow induced by the immersed body and the vortical wake. The combination of the nullspace approach and the multi-domain far-field boundary condition is found to be an order of magnitude faster than the original immersed boundary projection method. Furhter details are offered in [2].

Shown below is a numerical simulation based on our method. Here two cylinders approach each other with a vertical offset (Figure 2a). After collision, the cylinders move vertically away from each other (Figure 2b). Motion of the cylinders is prescribed for this example.

Figure 2: Two colliding cylinders with vorticity field shown with color contour for Re = 100. (a) left - before collision and (b) right - after collision. Movie (avi,1.9MB)

The immersed boundary method is also able to simulate flows aroung moving bodies. Here we consider a pair of flapping rectangular wings in freestream of Re=100. A vorticity profile from a coarse three-dimensional simulation is presented in Figure 3.

Figure 3: Flapping rectangular wings in freestream. Vortices shedding from the wings are shown by the isocontour. Movie (avi,0.8MB)

For Further Information

[1] K. Taira and T. Colonius, "The Immersed Boundary Method: A Projection Approach," Journal of Computational Physics, 225(2), 2118-2137, 2007.

[2] T. Colonius and K. Taira, "A Fast Immersed Boundary Method using a Nullspace Approach and Multi-Domain Far-Field Boundary Conditions," Computer Methods in Applied Mechanics and Engineering, 197, 2131-2146, 2008.

[3] K. Taira, W. B. Dickson, T. Colonius, M. H. Dickinson, and C. W. Rowley, "Unsteadiness in Flow over a Flat Plate at Angle-of-Attack at Low Reynolds Numbers," 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, Jan. 8-11, 2007 (AIAA 2007-710).

[4] K. Taira and T. Colonius, "Three-Dimensional Flows around Low-Aspect-Ratio Flat-Plate Wings at Low Reynolds Numbers," Journal of Fluid Mechanics, 2008 (submitted).

[5] K. Taira and T. Colonius, "On the Effect of Tip Vortices in Low-Reynolds-Number Post-Stall Flow Control," AIAA Journal, 2008 (to be submitted).

My list of publications can be found in my CV: pdf format.