Past Event: Oden Institute Seminar

Computational Methods for Collisional Transport: from Gas Dynamics to Mean Field Theory

Irene Gamba, Professor, Department of Mathematics and leader of the Oden Institute's Applied Mathematics Group

Abstract

The Boltzmann and Landau transport equation are at the core of statistical mechanics and physics when modeling meso-scales modeling the rarefied transport of particle undergoing interactions or collisions between particles of single or different species. Such collision operator are non-local with a bi-linear structure that enables particle mixing as much as classical conservation laws and entropy inequalities that control the decay rate to their steady equilibrium states. These models are naturally linked to classical fluid dynamics models that arise when their solutions are close to the statistical equilibrium given by Maxwell-Boltzmann distributions.
We will discuss two deterministic alternative computational techniques, namely a conservative-spectral scheme and a Galerkin-Petrov one, as much as their ability to capture phenomena due to boundary data that may not be well address neither by DSMC schemes nor by classical Navier Stokes equations for different problems raising from Mean Field Theory when coupling to the transportVlasov-Poisson system.
In addition, we will focus on error estimates for these collisional schemes and their applications to the Boltzmann for knock-on collisions, or Landau for Coulomb collisions operators and the ability to capture the expected decay rate to equilibrium as a function of intramolecular potentials. In addition we present a nw entropy stabilized method for a lid-driven cavity flow model with nonequilibrium conditions by a collisional solver in an approximation to Boltzmann moment closure yielding the Navier Stokes Fourier system with wall thermalization boundary conditions.
This is is work from several contributions in collaboration with R. Alonso, S.H. Tharkabhushanam, C. Zhang and J. Haack and C. Pennie for the conservative-spectral methods on Boltzmann and Landau models, and M. Abedelmalik, F. Baidoo, T. Hughes, T. Kessler and S. Rjasanow for the Galerkin-Petrov approach.
BIO Irene M. Gamba is Professor of Mathematics and leader of the Oden Institute's Applied Mathematics Group. She holds the W.A. “Tex” Moncrief, Jr. Chair in Computational Engineering and Sciences III. She earned her Ph.D. in mathematics at the University of Chicago in 1989 and held a National Science Foundation (NSF) postdoctoral fellowship at the Courant Institute at New York University, where she later became assistant and associate professor before coming to The University of Texas at Austin in 1997. Her scientific interests are analytical and computational issues in collisional kinetic theory include the evolution Boltzmann and Landau type equations in mean field regimes, gas mixture systems and quantum Boltzmann condensation in low temperatures regimes. Applications of these models range from plasma dynamics such as electron runaway transport, charged transport in nanodevices, approximations to classical fluid dynamics models and coupling of quantum gas system in the formation of condensates. Note: Please join this Zoom seminar online with the "Audio Only" function (no video)