Kinetic FRG Young Researchers Workshop
March 2-5, 2009

CSIC Building (#406), Seminar Room 4122.

Optimal Prediction for Radiative Transfer: A New Perspective on Moment Closure

Dr. Benjamin Seibold

Massachusetts Institute of Technology

Abstract: A direct numerical solution of kinetic equations is typically expensive, since the particle distribution depends on time, space and velocity. An expansion in the velocity variable yields an equivalent system of infinitely many moment equations. A fundamental problem is how to truncate the system. Various closures have been presented in the literature. Using the example of radiative transfer, we for­mulate the method of optimal prediction, a strategy to approximate the mean solution of a large system by a smaller system. To that end, the formalism is generalized to systems of partial differential equations. Using Gaussian measures, we re-derive linear closures, such as PN, diffusion, and diffusion correction closures. In addi­tion, new closures can be derived. We propose a crescendo-diffusion closure, which improves classical diffusion closures at no extra cost, as well as parabolic-type systems, similar to simplified PN closures.