Finite volume approximations of breakage population balance equation

In this work, a comparative study of two newly introduced numerical methods approximating the pure multiple breakage PBEs based on the finite volume scheme is performed. For a numerical scheme it is a very essential criterion to keep the total mass of the system constant. But approximating the pure multiple breakage PBEs by mid-point quadrature rules, it is found that the total mass does not remain constant. So, suitable adjustments are made in the discrete formulation such that the mass conservation is achieved. This idea has led to the development of a new mass conserving finite volume approximation of the pure multiple breakage PBEs. In some applications, besides conserving the total mass of the system, the estimation of the zeroth moment is of great importance. Therefore, some suitable adjustments are made in the scheme such that the zeroth moment is predicted as good as the exact result. Thus a new numerical method is obtained to approximate the pure multiple breakage PBEs. Several test problems are considered in order to assess the accuracy of the two different schemes numerically.