Abstract:
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. |