Improved accuracy and convergence analysis of finite volume methods for particle fragmentation models

Abstract

In this work, two new number-and volume-consistent finite volume methods for the numerical solution of binary and multifragmentation problems are introduced. The new number-consistency is achieved by introducing a single weight function. Several benchmark problems of different complexity are solved to assess the accuracy. Mathematical convergence analysis suggests that both of the new methods are numerically second order convergent with respect to the grid size on uniform and nonuniform meshes.

Conservative Finite Volume Schemes for Multidimensional Fragmentation Problems

“…As a prototype, consider the conservative formulation of the multiple fragmentation equation given by [22,23]: The initial value problem for t ≥ 0 is formulated as ∂g(t, x) ∂t = ∂H(t, x) ∂x , where x ∈ R + := (0, ∞),…”