Collective Behavior: Macroscopic versus Kinetic Descriptions

Conservative numerical schemes for non-linear kinetic equations

Irene Gamba

University of Texas at Austin

We will present an overview of novel numerical methods for nonlinear models of kinetic statistical flows type. These models share the feature of preservation of flow invariant quantities. Examples to be discussed are the classical non-linear Boltzmann equation for Coulombic interactions and grazing collision limits to the Landau equation, as well as a kinetic description of the Vicsek swarming model.

We will describe some deterministic conservative solvers that enable rigorous stability, convergence and error analysis, and present numerical simulations.

These is work in collaboration with Jeff Haack, the Viczek model is also in collaboration with Pierre Degond and Sebastien Motsch.