His research goal is to develop accurate and efficient numerical methods for computational problems in science and engineering. The methods he works on typically use the Green’s function to convert the relevant differential equation into an integral equation. Krasny develops treecode algorithms for efficient computation of long-range particle interactions. Topics of interest include fluid dynamics (vortex sheets, vortex rings, Hamiltonian chaos, geophysical flow), and electrostatics (Poisson-Boltzmann model for solvated proteins). He is also interested in modeling charge transport in organic solar cells.
This picture illustrates the instability of a vortex ring. The ring was modeled as a circular disk vortex sheet with an imposed perturbation of azimuthal wavenumber m=8. The ring’s motion was computed using a Lagrangian particle method and a treecode algorithm for fast evaluation of the induced velocity. The picture shows three isosurfaces of vorticity at a late time in the simulation. The results reveal details of the instability, in particular the relation between axial flow and collapse of the vortex core.
