SIAM Journal on Scientific Computing, Volume 42, Issue 6, Page B1570-B1598, January 2020.
The study of collision-induced nonlinear breakage phenomenon is mostly unexplored but is important in the area of particulate processes. In this work, the volume and time dependent collisional breakage kernel function is modeled based on the population balance modeling approach. To solve the nonlinear breakage population balance equation, the weighted finite volume scheme for linear breakage process from Kumar, Saha, and Tsotsas [SIAM J. Numer. Anal., 53 (2015), pp. 1672--1689] is extended for the case of collision-induced breakage process. The weighted finite volume scheme is developed in such a way that it conserves the total mass of the system while preserving the total number of particles in the system. Moreover, an event-driven constant number Monte Carlo simulation algorithm is presented, and the simulation results are used as an alternative to experimental results. The volume dependency of the collisional breakage kernel is incorporated successfully in the Monte Carlo simulation for the first time while selecting particles for collision events. Some essential properties of any particulate process, such as the total number of particles and the size distribution of particles, are validated successfully for several breakage distribution functions using the Monte Carlo results. This offers new insights into the estimation and interpretation of collision-induced nonlinear breakage kinetics.

中文翻译：

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非线性破损种群平衡方程核的近似解和建模

SIAM科学计算杂志，第42卷，第6期，第B1570-B1598页，2020年1月。
碰撞诱发的非线性破坏现象的研究大多尚未探索，但在颗粒过程领域很重要。在这项工作中，基于总体平衡建模方法对体积和时间相关的碰撞破坏核函数进行了建模。为了解决非线性破损种群平衡方程，使用了来自Kumar，Saha和Tsotsas的线性破损过程的加权有限体积方案[SIAM J. Numer。Anal。，53（2015），pp。1672--1689]扩展了碰撞引起的断裂过程的情况。加权有限体积方案的开发方式是，它既保留了系统的总质量，又保留了系统中的粒子总数。此外，提出了一种事件驱动的常数蒙特卡罗模拟算法，仿真结果代替了实验结果。在选择碰撞事件的粒子时，碰撞破坏核的体积依赖性首次成功地纳入了蒙特卡洛模拟。使用蒙特卡洛结果，已成功验证了几种颗粒过程的一些基本属性，例如颗粒总数和颗粒尺寸分布，可用于多种破损分布函数。这为碰撞引起的非线性破坏动力学的估计和解释提供了新的见识。使用蒙特卡洛结果，已成功验证了几种颗粒过程的一些基本属性，例如颗粒总数和颗粒尺寸分布，可用于多种破损分布函数。这为碰撞引起的非线性破坏动力学的估计和解释提供了新的见识。使用蒙特卡洛结果，已成功验证了几种颗粒过程的一些基本属性，例如颗粒总数和颗粒尺寸分布，可用于多种破损分布函数。这为碰撞引起的非线性破坏动力学的估计和解释提供了新的见识。