2.2.3 Closure Problem

Macroscopic models are obtained by taking the system of moment equations and truncating it at a suitable order $N$. Such a truncation introduces three main problems due to the fact that the number of unknowns exceeds that of the equations. These are

1. Elimination of additional lower order moments which appear in the equations: These moments can be eliminated in the framework of the diffusion approximation.
2. Closure for terms involving the scattering operator
3. Closure for the highest order moment: This is the topic of Chapter 3.

The main emphasis in this thesis is put on studying different kinds of closure relations for the highest order moments. In our case this is the sixth moment $M_6$.