An efficient implementation of a conservative finite volume scheme with constant and linear reconstructions for solving the coagulation equation

Population balances provide an economic means of describing dense particulate phases with particle-particle interactions. Here, we focus on particle coagulation and address the evaluation of the corresponding integral source terms within the scope of a conservative finite volume formulation. Based on one kernel evaluation for every pair of parent cells, efficient analytical formulas are derived that obviate the explicit decomposition of the integration domains into elementary geometrical shapes and are valid for arbitrary volume-grids. Considering the volume-weighted cell averages as degrees of freedom, the formulas are presented for both cell-wise constant and linear reconstructions of the particle volume distribution. We find the latter to be effective at mitigating the unphysically heavy tails that are characteristic of solutions obtained with piecewise constant reconstructions. For Brownian coagulation, the computational expense is mainly caused by the kernel evaluations, while the cost of the parent-daughter pairing and integration algorithm is almost negligibly small.

Automated summary

Population balances are used to describe dense particulate phases with particle-particle interactions. In this study, we focus on particle coagulation and develop efficient analytical formulas for evaluating source terms within a finite volume framework. These formulas eliminate the need for explicit decomposition of integration domains and are applicable to any volume-grids. The study also proposes cell-wise constant and linear reconstructions of particle volume distribution to mitigate unphysical heavy tails.