Moments preserving finite volume approximations for the non-linear collisional fragmentation model

Abstract

We present the development of approximate numerical schemes to solve the non-linear fragmentation model. Two numerical weighted finite volume techniques are presented based on the particulate system’s mass and number preservation properties. In addition, we have extended the results for multi-dimensional formulation. A detailed discussion on mathematical convergence analysis and consistency is exhibited under some regulations on the collision kernels and initial data. It is shown that the developed schemes mathematically possess a second-order convergence rate irrespective of the mesh type. Several numerical examples are presented to validate the proficiency and accuracy of the developed schemes.