标题： 多维建模下碰撞破碎方程的截面体积平均法的收敛率与误差分析 显示英文标题

标题： Convergence-rate and error analysis of sectional-volume average method for the collisional breakage equation with multi-dimensional modelling

摘要： 近期文献报道了两种求解一维碰撞诱导的非线性颗粒破碎方程的截断技术：有限体积法 [Das 等，2020，SIAM J. Sci. Comput., 42(6): B1570-B1598] 和固定枢轴技术 [Kushwah 等，2023，Commun. Nonlinear Sci. Numer. Simul., 121(37): 107244]。研究发现这两种方法在随机网格上都变得不一致。因此，我们提出了一种新的出生修正策略，在该策略中，新生成的颗粒根据每个细胞的平均体积按比例分配到三个相邻的单元格中。这种修改技术通过使其在随机网格上保持一致性来改进数值模型。针对均匀、非均匀、局部均匀、随机和振荡网格的不同可能选择，对该新方案进行了详细的收敛性和误差分析。此外，我们还确定了核函数的条件，这些条件下收敛率显著提高，并且该方案在均匀、非均匀和局部均匀网格上达到二阶收敛。更高的精度将使新模型能够轻松与CFD模块耦合。文献中的另一项重大进展是通过在矩形网格上扩展二维方程的离散模型实现的。 显示英文摘要

摘要： Recent literature reports two sectional techniques, the finite volume method [Das et al., 2020, SIAM J. Sci. Comput., 42(6): B1570-B1598] and the fixed pivot technique [Kushwah et al., 2023, Commun. Nonlinear Sci. Numer. Simul., 121(37): 107244] to solve one-dimensional collision-induced nonlinear particle breakage equation. It is observed that both the methods become inconsistent over random grids. Therefore, we propose a new birth modification strategy, where the newly born particles are proportionately allocated in three adjacent cells, depending upon the average volume in each cell. This modification technique improves the numerical model by making it consistent over random grids. A detailed convergence and error analysis for this new scheme is studied over different possible choices of grids such as uniform, nonuniform, locally-uniform, random and oscillatory grids. In addition, we have also identified the conditions upon kernels for which the convergence rate increases significantly and the scheme achieves second order of convergence over uniform, nonuniform and locally-uniform grids. The enhanced order of accuracy will enable the new model to be easily coupled with CFD-modules. Another significant advancement in the literature is done by extending the discrete model for two-dimensional equation over rectangular grids.