Simulation of Transport in Transition Regimes

Technology is increasingly advancing into regimes in which particle mean-free paths are comparable to the length scales of interest, and where traditional transport models therefore break down. For example, drift-diffusion models of electron-hole transport break down for submicron semiconductors because the scale of interest are very small, while Navier-Stokes approximations of fluid dynamics break down in outer planetary atmospheres or space shuttle reentry problem, where the mean free path are very large.

Such situations can be described by particle simulations but the cost of carrying these out is much greater than that of small mean-free path models, often becoming prohibitive when one is near small mean-free path regimes. This makes the simulation of problems in which transition regimes coexist with small mean-free path regimes particularly difficult. This difficulty is compounded when the geometry is complicated or even random.

This workshop will explore a variety of advanced models such us moment based models, Chapmann-Enskog and Burnett type expansions, or models derived from asymptotic limits. These models, both deterministic and stochastic in origin, will be studied in the context of the simulation of high-altitude flight, charged particles in natural plasmas such us outer planetary atmospheres, man-made plasmas (electric propulsion for satellites), electron and holes in semiconductor devices, and radiation through inhomogeneous media. Hybrid numerical schemes that properly match transition with small mean-free path regimes will also be examined.