Abstract In this present work, a finite volume scheme for approximating a multidimensional nonlinear agglomeration population balance equation on a regular triangular grid is developed. The finite volume schemes developed in literature are restricted to a rectangular grid [43]. However, the accuracy and efficiency of finite volume scheme can be enhanced by considering triangular grids. The triangular grid is generated using the concept of ‘Voronoi Partitioning’ and ‘Delaunay Triangulation’. To test the accuracy and efficiency of the scheme on a triangular grid, the numerical results are compared with the sectional method, namely Cell Average Technique [38] for various analytically tractable kernels. The results reveal that the finite volume scheme on a triangular grid is computationally less expensive and predicts the number density function along with the different order moments more accurately than the cell average technique. Furthermore, the numerical comparison is extended by comparing the finite volume scheme on a rectangular grid. It also demonstrates that the finite volume scheme with a regular triangular grid computes the numerical results more accurately and efficiently than the finite volume scheme with a rectangular grid.

中文翻译：

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三角网格上非线性团聚人口平衡方程的有限体积近似

摘要 在目前的工作中，开发了一种在规则三角网格上逼近多维非线性聚集人口平衡方程的有限体积方案。文献中开发的有限体积方案仅限于矩形网格 [43]。但是，可以通过考虑三角形网格来提高有限体积方案的精度和效率。三角形网格是使用“Voronoi Partitioning”和“Delaunay Triangulation”的概念生成的。为了在三角形网格上测试该方案的准确性和效率，将数值结果与分段方法进行比较，即各种可解析内核的单元平均技术 [38]。结果表明，三角形网格上的有限体积方案在计算上成本较低，并且比单元平均技术更准确地预测数密度函数以及不同阶矩。此外，通过比较矩形网格上的有限体积方案来扩展数值比较。它还表明，与具有矩形网格的有限体积方案相比，具有规则三角形网格的有限体积方案计算数值结果更准确、更有效。