A numerical scheme based on the finite volume approach is developed to solve a binary breakage population balance equation (PBE) on nonuniform meshes. The key feature of the new scheme is that it is free of the common requirement of redistributing the particle mass to neighboring pivots, its formulation is simpler compared to other methods such as cell average and fixed pivot techniques. The new scheme produces accurate results for the distribution and its first two moments while consuming less computational time. The accuracy and efficiency of the proposed scheme is validated against the recently developed volume conserving finite volume scheme for various benchmark problems. We prove that convergence exhibits second-order consistency and confirm the conclusion by numerical calculation of the experimental order of convergence in different meshes. The new approximation is the first ever two-order moment conserving finite volume scheme for a binary breakage PBE that is free from constraint that the particles are concentrated on the representative of the cell.

提出了一种基于有限体积方法的数值方案，用于求解非均匀网格上的二元破损总体平衡方程（PBE）。新方案的关键特征是它没有将粒子质量重新分配给相邻枢轴的一般要求，与其他方法（例如像元平均和固定枢轴技术）相比，它的制定更加简单。新方案可为分配及其前两个时刻产生准确的结果，同时消耗更少的计算时间。针对各种基准问题，针对最近开发的体积守恒有限体积方案，验证了所提出方案的准确性和效率。我们证明了收敛表现出二阶一致性，并通过对不同网格中收敛实验顺序的数值计算来证实结论。