Past Event: Oden Institute Seminar

Conservative spectral methods for solving the Boltzmann transport equation

Jeff Haack, Department of Mathematics, UT Austin

Abstract

The Boltzmann transport equation models the dynamics of a dilute gas of particles that are not in thermodynamic equilibrium. The main difficulty in numerically simulating this equation is the collisional term, which takes the form of a high-dimensional, nonlinear, nonlocal integral operator. Previously this term was too expensive to compute with deterministic methods, requiring stochastic particle methods to find an approximation of the dynamics of the system. However, recent developments working with the Fourier transform of the operator can compute this term to high accuracy while reducing the computational cost to a manageable amount of time, which allows computation of many problem regimes that are not well-suited to particle methods, as well as avoiding the noise inherent in stochastic methods. In addition, this formulation is very suitable for parallelization, and I will present preliminary results investigating the scaling of the method to massively parallel systems. Finally, I will present numerical results near the singular grazing collisions (Landau) limit of plasma physics as well as the extension to multi species gases and internal energy excitation. This is joint work with Irene Gamba (Texas) and Thierry Magin and Alessandro Munafo (Von Karman Institute).