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首页> 外文期刊>Journal of Computational Physics >Accurate and efficient approximations for generalized population balances incorporating coagulation and fragmentation
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Accurate and efficient approximations for generalized population balances incorporating coagulation and fragmentation

机译：用于凝结和碎片的广义人口平衡的准确和有效的近似

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摘要

This study focuses on development of two approaches based on finite volume schemes for solving both one-dimensional and multidimensional nonlinear simultaneous coagulation fragmentation population balance equations (PBEs). Existing finite volume schemes and sectional methods such as fixed pivot technique and cell average technique have many issues related to accuracy and efficiency. To resolve these challenges, two finite volume schemes are developed and compared with the cell average technique along with the exact solutions. The new schemes have features such as simpler mathematical formulations, easy to code and robust to apply on nonuniform grids. The numerical testing shows that both new finite volume schemes compute the number density functions and their corresponding integral moments with higher precision on a coarse grid by consuming lesser CPU time. In addition, both schemes are extended to approximate generalized simultaneous coagulation fragmentation problems and retains the numerical accuracy and efficiency. For the higher dimensional PBEs (2D and 3D), the investigation and verification of the numerical schemes is done by deriving new exact integral moments for various combinations of coagulation kernels, selection functions and fragmentation kernels. (c) 2021 Elsevier Inc. All rights reserved.
机译：本研究的重点是开发两种基于有限体积格式的方法，用于求解一维和多维非线性同时混凝-碎裂人口平衡方程（PBE）。现有的有限体积法和剖分法，如固定支点法和单元平均法，存在许多与精度和效率有关的问题。为了解决这些挑战，我们开发了两种有限体积格式，并与单元平均技术以及精确解进行了比较。新方案具有数学公式简单、易于编码、适用于非均匀网格等特点。数值试验表明，这两种新的有限体积格式在粗网格上计算数密度函数及其相应的积分矩的精度更高，占用的CPU时间更少。此外，两种格式都被推广到近似广义同时混凝破碎问题，并保持了数值精度和效率。对于高维PBE（2D和3D），通过推导凝聚核、选择函数和碎裂核的各种组合的新的精确积分矩，对数值格式进行了研究和验证。（c）2021爱思唯尔公司保留所有权利。

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