Mini-Workshop: Numerics for Kinetic Equations

Abstract

Kinetic equations are crucial to an adequate description of many processes of scientific and industrial importance. In recent years there have been intensified research activities in the field of numerical algorithms for kinetic equations related to new areas of application. Typical gas flows in micro- and nanomachines are in the rarefied regime. Thus the classical Boltzmann equation is often used to model such flows. Furthermore, the inelastic Boltzmann equation describes low density flows of granular material. Finally, flows of electrically charged particles are described by semiconductor transport equations. There are significant numerical challenges related to these applications. In low Mach number rarefied flows there is a very small signal-to-noise ratio. Therefore, variance reduction techniques for the commonly used Direct Simulation Monte Carlo method are needed. On the other hand, deterministic algorithms become more competitive. The workshop brought together leading experts from various fields to discuss recent approaches addressing the numerical challenges related to the novel applications mentioned above.