I'm interested in developing more accurate and efficient algorithms for computer simulations in fluid dynamics and molecular dynamics. The work involves designing an algorithm, writing a computer code, and running the code to gain insight into the physics or mathematics. A longstanding goal is to simulate vortex sheet motion which is relevant to the stability of wakes, for example the wake of a fish or an aircraft. The problem is challenging because it exhibits singularity formation and chaotic dynamics. The methods I use are based on the Green's function of the Laplace operator or a related PDE, and they use adaptive quadrature schemes to evaluate convolution integrals. In particular I developed new techniques for treecode algorithms which compute the forces acting among a set of particles exhibiting long-range interactions.
Current projects include
1) a particle method for fluid flow on a rotating sphere with applications to atmosphere and ocean dynamics,
2) the electrostatic potential of a solvated biomolecule using the Poisson-Boltzmann implicit solvent model, and
3) a drift-diffusion model for organic solar cells.