New finite volume approach for multidimensional Smoluchowski equation on nonuniform grids

This present work is based on developing a deterministic discrete formulation for the approximation of a multidimensional Smoluchowski (Coalescence) equation on a nonuniform grid. The mathematical formulation of the proposed method is simpler, easy to implement, and focuses on conserving the first-order moment. The new scheme resolved the issue of mass conservation along individual components in contrast to the existing scheme which focuses only on conservation of the total mass of all components. The validation of the new scheme is conducted against the existing scheme by considering some classical tests. The comparison reveals that the new scheme has the ability to compute the higher-order moments with higher accuracy than the existing scheme on a coarse grid without taking any specific measures. For the higher-dimensional population balance equations, the mixing of components quantified using chi 2 parameter is also computed accurately and efficiently using a very coarse nonuniform grid.

Automated summary

This study focuses on developing a deterministic discrete formulation for approximating the multidimensional Smoluchowski (Coalescence) equation on a nonuniform grid. The proposed method is simpler, easy to implement, and emphasizes conserving the first-order moment. Tests show that the new scheme can compute higher-order moments with higher accuracy on a coarse grid compared to the existing scheme.