Development and analysis of moments preserving finite volume schemes for multi-variate nonlinear breakage model

Abstract

Modelling and simulation of collisional particle breakage mechanisms are crucial in several physical phenomena (asteroid belts, molecular clouds, raindrop distribution etc.) and process industries (chemical, pharmaceutical, material etc.). This paper deals with the development and analysis of schemes to numerically solve the multi-dimensional nonlinear collisional fragmentation model. Two numerical techniques are presented based on the finite volume discretization method. It is shown that the proposed schemes are consistent with the hypervolume conservation property. Moreover, the number preservation property law also holds for one of them. Detailed mathematical discussions are presented to establish the convergence analysis and consistency of the multi-dimensional schemes under predefined restrictions on the kernel and initial data. The proposed schemes are shown to be second-order convergent. Finally, several numerical computations (one-, two- and three-dimensional fragmentation) are performed to validate the numerical schemes.