Rate of convergence of two moments consistent finite volume scheme for non-classical divergence coagulation equation

Abstract

This study focuses on performing a convergence analysis of the recently developed mass based finite volume scheme [20] to simulate a Smoluchowski coagulation equation. The goal of this method is to retain the total number of particles in the system while maintaining a constant mass of the particles utilizing some weights in the formulation. The Lipschitz continuity and consistency of the MBFVS are examined and investigated thoroughly by providing theorems. The rate of convergence of the MBFVS is investigated on (a) uniform grid, (b) non-uniform smooth (geometric) grid, and (c) locally uniform grid. The numerical results in term of number density function and its moments are computed and compared with exact results to ensure the authenticity of the scheme for gelling kernels. In comparison to the sectional approaches such as fixed pivot technique (Giri and Hausenblas, 2013 [13]) and cell average technique (Giri and Nagar, 2015 [14]), this scheme is the best candidate for coupling with powerful tools such as CFD, Ansys, and gPROMS due to its simplified formulation, robust implementation on any grid and coagulation kernel, second order convergence rate and consistency with two moments.