Young Researchers Workshop:
Kinetic and macroscopic models for complex systems

Matching Boundary Conditions for Moment Systems

Weiran Sun

Simon Fraser University

Kinetic equations are widely used to describe the evolution of particle den- sity functions. Computationally these equations can be expensive when there are many particles involved. Moment closures are developed as reductions of kinetic equations. These equations can be viewed as macroscopic models which govern various moments of density functions. A physically and computationally meaningful question is how to de- rive compatible boundary conditions for moment closures when given certain boundary conditions for the underlying kinetic equation. In this talk we give a general derivation of boundary conditions for moment systems that are derived from linear or linearized kinetic equations with incoming data. This derivation can be applied to various types of kinetic equations such as the linear neutron transport equations and the linearized Boltzmann equation. For simple stationary systems we will show the well-posedness and accuracy of the moment systems with the so-derived boundary conditions.