This work is focused on developing a finite volume scheme for approximating a fragmentation equation. The mathematical analysis is discussed in detail by examining thoroughly the consistency and convergence of the numerical scheme. The idea of the proposed scheme is based on conserving the total mass and preserving the total number of particles in the system. The proposed scheme is free from the trait that the particles are concentrated at the representative of the cells. The verification of the scheme is done against the analytical solutions for several combinations of standard fragmentation kernel and selection functions. The numerical testing shows that the proposed scheme is highly accurate in predicting the number distribution function and various moments. The scheme has the tendency to capture the higher order moments even though no measure has been taken for their accuracy. It is also shown that the scheme is second-order convergent on both uniform and nonuniform grids. Experimental order of convergence is used to validate the theoretical observations of convergence.

这项工作的重点是开发一种有限体积方案，用于近似一个碎片方程。通过彻底检查数值方案的一致性和收敛性，详细讨论了数学分析。所提出的方案的思想是基于节省总质量并保留系统中粒子的总数。所提出的方案没有颗粒集中在细胞代表的特征。针对标准片段化内核和选择功能的几种组合的解析解决方案，对该方案进行了验证。数值测试表明，该方案在预测数分布函数和各种矩时具有很高的精度。即使没有针对其精度采取任何措施，该方案也有捕获高阶矩的趋势。还表明该方案在均匀和非均匀网格上都是二阶收敛的。收敛的实验顺序用于验证收敛的理论观察。