Young Researchers Workshop: Kinetic models in biology and social sciences

A Conservative, Entropic Multispecies BGK Model

Jeff Haack

Los Alamos National Laboratory


We derive a conservative multispecies BGK model that follows the spirit of the original, single species BGK model by making the specific choice to conserve species masses, total momentum, and total kinetic energy and to satisfy Boltzmann’s H-Theorem. The derivation emphasizes the connection to the Boltzmann operator which allows for direct inclusion of information from higher-fidelity collision physics models. We numerically investigate velocity and temperature relaxation in dense plasmas and compare the model with previous multispecies BGK models and discuss the trade-offs that are made in defining and using them. In particular, we demonstrate that the BGK model in the NRL plasma formulary does not conserve momentum or energy in general. We then apply the model to a warm dense matter scenario in which the ablator-fuel interface of an inertial confinement fusion target is heated. In our numerical results we compare the relative size of various diffusion components (Fickean diffusion, electrodiffusion, and barodiffusion) as the interface evolves and we examine `kineticness' in order to determine when this problem can be described with a hydrodynamic model.