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
