Multiscale Computations for Kinetic and Related Problems

Grad’s Method of Moments, and Beyond

Henning Struchtrup

University of Victoria

The method of moments aims at finding macroscopic transport equations for rarefied gas flows, which are derived from the Boltzmann equation of kinetic theory. Harold Grad pioneered this approach in 1949, with further discussion in his contribution to the Encyclopedia of Physics (1958); Grad’s 13 Moment Equations are well known . In this talk, I will outline the ideas of Grad’s method, its capabilities and limitations in describing phenomena in rarefied gases, and its connection to other approaches, such as the Chapman-Enskog expansion, and theories of Extended Thermodynamics. Some emphasis will be on my research, with colleagues and students, on the Regularized 13 Moment Equations (R13), which shed new light on the moment method. It will be shown that, similar to the Chapman-Enskog method, Knudsen number orders can be used to identify the moments required, and their governing equations, at the desired order. Boundary conditions are discussed as well, and results for a number of boundary value problems are considered as test cases.