Kinetics-based finite-volume methods
In this appendix we discuss the solution of the moment-transport equations found from the GPBE using kinetics-based finite-volume methods (KBFVM) in multiple spatial dimensions. As in Section 8.2, the discussion focuses on time advancement using a single-stage Euler explicit time-integration scheme. Readers interested in more details on finite-volume methods are referred to Leveque (2002).
B.1 Spatial dependence of GPBE
In the following, we denote the NDF by n(t, x, v, ξ), where the velocity internal coordinates are v and the remaining internal coordinates are ξ. The general form of the GPBE to be considered is
where the second and third terms on the left-hand side are multidimensional ...