Accurate and efficient flux-corrected finite volume approximation for the fragmentation problem

Abstract

In this work, we introduce a weighted finite volume scheme for multiple fragmentation problems and report a convergence criterion of the scheme. It is observed that the finite volume method mentioned in Kumar and Kumar (Appl Math Comput 219(10):5140– 5151, 2013) has not estimated the physical moments of clusters with satisfactory precision. Therefore, to control this deficiency, a weight function, and a correction factor are introduced in the numerical flux to approximate the conservative formulation of the multiple fragmentation equation. The proposed scheme preserves the first two physical moments with high accuracy in the cell overlapping case for newly born clusters. It is shown that the new formulation converges weakly under certain growth restrictions on the kernels. Finally, simulation results and numerical validations are presented