Upcoming Event: PhD Dissertation Defense

The Variational Multiscale Moment Method for the Boltzmann Equation

Frimpong A. Baidoo, CSEM Ph.D. Candidate, Oden Institute

Abstract

A novel framework for deriving systems of conservation equations from the Boltzmann equation, based on the Variational Multiscale Method, is described. The framework is then used to derive an entropy stable extension to the Navier-Stokes-Fourier equations for rarefied gas flow. With the aid of Burnett functions, the fluid parameters for these equations are computed for the Hard Spheres and Maxwell Molecules collision models. Analytical solutions to these entropy stable equations in a one-dimensional channel are then compared to those of the linearized Boltzmann equation with diffuse reflection boundary conditions. The implied distribution function of this entropy stable extension is also compared to a highly refined numerical solution to the linearized Boltzmann equation. In both cases, the solution due to the entropy stable extension is shown to be remarkably close to that of the linearized Boltzmann solution, outperforming the corresponding Navier-Stokes-Fourier solutions. In order to compute the non-linear version of this entropy stable extension, an identity for the derivative of the inverse linearized collision operator is described and used in the computation of closures. In the process, a simpler set of equations that maintain entropy stability are also derived from the original entropy stable extension.

Biography

Baidoo majored in Physics and Mathematics at the University of Chicago in 2018 and joined the Oden Institute in the same year. He is co-advised by Tom Hughes and Irene Gamba.