Research Interests

My general research interests are in Computational Fluid Dynamics and Low Reynolds Number Hydrodynamics. Currently, I am working on developing integral equation methods to solve the Stokes and the Navier-Stokes Equations in fluid dynamics. An integral equation is a way of expressing the governing equations in terms of quantities contained on the boundary of the flow domain. These integral equation methods, when coupled with modern fast algorithms, have a significant advantage over conventional approaches for solving flow problems in complicated domains. For example, computing the flow past a large number of particles of arbitrary shape or modelling the deformation of a gas bubble in a fluid are much more easily done by discretizing equations given on the boundary rather than throughout the entire fluid domain.

With these computational methods, I also investigate physical phenomena in low Reynolds number flow. A low Reynolds number corresponds to slow-moving, highly viscous fluids or flows past objects with very small length scales (i.e. microorganisms and dust particles). Examples of problems that can be investigated are: the flow of water and oil through soil, sedimentation of sand in river beds, the flow of blood in capillaries, and the motion and deformation of liquid drops and bubbles. Problems of this type arise in many important applications in engineering such as: elimination of atmospheric pollution, sedimentation of slurries and ground water hydrology.