Efficient numerical schemes for multidimensional population balance models

Multidimensional population balance models (PBMs) describe chemical and biological processes having a distribution over two or more intrinsic properties (such as size age, independent spatial variables). The incorporation of additional variables into PBM improves its descriptive capability can be necessary to capture specific features interest. As most PBMs interest cannot solved analytically, computationally expensive high-order finite difference volume methods are frequently used obtain an accurate numerical solution. We propose scheme based on operator splitting solving each sub-problem at the limit stability that achieves discretization error is zero for certain classes low enough acceptable other classes. In conjunction employing specially constructed meshes variable transformations, exploits commutative property differential operators present in many PBMs. has very computational cost — potentially just memory reallocation. Multiple case studies demonstrate performance proposed scheme.