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

IF 1.9 3区 数学 Q2 Mathematics
Mehakpreet Singh, Gavin Walker, V. Ranade
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引用次数: 8

Abstract

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.
减少碎片模型新方法的制定与收敛性分析:解聚的实例应用
在这项工作中,两个基于有限体积方法的离散公式被开发为一个减少碎片模型。通过对选择函数的修改,实现了质量守恒和零阶矩的精确预测等重要特性。该方法可以在不采取任何具体措施的情况下以较高的精度计算二阶矩,这在实际应用中对粒子的面积预测起着重要作用。对两种格式在Lipschitz条件和一致性条件下的收敛性进行了深入的分析,并显示出二阶收敛性。将这两种方案应用于聚合物科学和化学工程中常见的解聚问题,证明了它们的准确性和有效性。结果表明,新格式易于实现,计算效率高,即使在较粗糙的网格上也能以较高的精度计算数值结果。
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来源期刊
CiteScore
2.70
自引率
5.30%
发文量
27
审稿时长
6-12 weeks
期刊介绍: M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.
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