Numerical Methods for Plasma Astrophysics:
From Particle Kinetics to MHD

CSIC Building (#406), Seminar Room 4122.
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Fluid Moment Closures Used in Lattice Boltzmann Methods for Landau Damping

Dr. Angus MacNab

CSCAMM at University of Maryland

Abstract:   In searching for an appropriate median between fluid and kinetic modeling techniques, Lattice Boltzmann Methods (LBMs) stand out as an interesting scheme because of their computational efficiency, as compared against other fluid modeling techniques, and the underlying kinetic algorithm which governs the evolution of the fluid variables. LBMs retain the full dimensionality of kinetic methods, but reduce the breadth of particle velocity space so that only two or three speeds are allowed in any given direction. The algorithm solves a discrete BGK Boltzmann equation in Cartesian space for each of the allowable particle velocities. Macroscopic fluid moments are then recovered from the summation of the particle distribution functions over the allowed velocities. A clear advantage of the LBM formulation of these fluid equations comes from the kinetic nature of the scheme. In the space of the particle distribution functions, all of the convective fluid derivatives are treated with a single linear advection step. This allows for a full non-linear description of the fluid equations. We will present one-dimensional models, which incorporate non-local integral closures into the particle distribution functions. These models serve as an elementary demonstration of the viability and tractability of the incorporation of non-local kinetic closures into LBMs. Results are presented for models closed at the level of particle flux (velocity), momentum flux (pressure), and heat flux.