Young Researchers Workshop:
Kinetic and macroscopic models for complex systems

Moment realizability-based numerical method for multi-scale kinetic equations

Thomas Rey

University of Maryland

Many engineering problems involve fluids in transitional regimes (micro-electro-mechanical-systems, space shuttle reentry, ...). In these cases, the Euler or Navier-Stokes-like fluid description breaks down, typically due to shocks or boundary layers, and the use of a kinetic equation is needed to describe accurately the system. Nevertheless, this type of description is computationally expansive, and it is desirable to use it only locally, thanks to hybrid kinetic/fluid schemes. In this joint work with F. Filbet, I will present a new type of hybrid scheme, using the so-called moment realizability criterion (due to Levermore, Morokoff and Nadiga) to identify the kinetic zones, and apply it to many different multi-scales problems