Moment Closure Methods for Kinetic Equations of Complex Transport Phenomena and their Numerical Solution

Instructor: Professor C. P. T. Groth

Gaspard Monge Visiting Professor
Centre de Mathematiques Appliquees (CMAP), École Polytechnique

University of Toronto Institute for Aerospace Studies (UTIAS)
E-mail: groth@utias.utoronto.ca
Home page: http://arrow.utias.utoronto.ca/~groth/

Course URL: http://arrow.utias.utoronto.ca/~groth/moment-closure-course

Course Description

Moment closure methods are considered for kinetic equations governing a range of complex transport phenomena, including non-equilibrium, rarefied, gaseous flow phenomena as described by the Boltzmann kinetic equation, multi-phase poly-disperse spray behaviour described by the Williams-Boltzmann equation, and radiative heat transfer in non-gray, participating media as described by the radiative transfer equation. Moment closure methods offer a means of significant complexity reduction when constructing approximate solutions to such high-dimensional equations, providing a good compromise between computational efficiency and accuracy for many practical engineering applications. Closure techniques based on classical Grad-type methods, maximum-entropy considerations, as well as quadrature formulations will all be considered. The numerical solution of the resulting systems of hyperbolic moment equations that result from the moment closure strategy will also be examined. Course syllabus.

Lectures

Thursday, 2:00 pm - 5:00 pm, École Polytechnique, February 27 - April 9, 2020.

Lecture Notes

Course syllabus is available here.
Lecture notes are available here.

Practice Problems

Practice problems are available here.