Formulation and Convergence Analysis of New Methods for Reduced Fragmentation Model: Illustrative Application to Depolymerization

In this work, two discrete formulations based on the finite volume approach for a reduced fragmentation model are developed. The important features such as mass conservation and accurate prediction of the zeroth order moments are accomplished by the modification of the selection function. The new schemes can compute the second order moment, which plays a significant role in predicting the area of the particles in real life applications, with high accuracy without taking any specific measures. A thorough convergence analysis of both schemes including Lipschitz condition and consistency is presented and exhibit second order convergence. The accuracy and efficiency of both schemes is demonstrated by applying them to the depolymerization problem which commonly arises in polymer sciences and chemical engineering. It is demonstrated that the new schemes are easy to implement, computationally efficient and able to compute the numerical results with higher precision even on a coarser grid.