Biomechanics of insect respiration
Insects, and most terrestrial arthropods, breathe using complex network of inelastic, but collapsible tracheal tubes. This may be nature's paradigm for gas transport at the microscale.
Geophysical flow closure models
Large eddy simulations (LES) reduce the spatial and temporal complexity of turbulent flow computations by modeling the contributions of the small scales, which are assumed to be the same for every turbulent flow. Most such closure models are derived based on heuristic assmuptions based on the physics of 3D turbulent flows. We are developing and applying purely mathematical closure models, which may be more appropriate for geophysics flows, which are approximately 2D.
Coarse grid projection method for incompressible flows
A major subset of computational methods for solving the Navier-Stokes equations, the equations that govern fluid dynamics, are projection methods that decouple the computations of the pressure and velocity fields. We have developed a grid projection method that solves the pressure part of the problem on a coarse grid, and interpolates the results back to a fine grid to compute the velocity field. The method has been shown to drastically reduce the computational effort , with little to no reduction in the accuracy of the velocity field.