Mathematical analysis of finite volume preserving scheme for nonlinear Smoluchowski equation

This study presents the convergence analysis of the recently developed finite volume preserving scheme (Forestier-Coste and Mancini, 2012) for approximating a coalescence or Smoluchowski equation. The idea of the finite volume scheme is to preserve the total volume in the system by modifying the coalescence kernel using the notion of overlapping bins (cells). The consistency of the finite volume scheme is examined thoroughly in order to prove second-order convergence on uniform, non-uniform smooth and locally uniform grids independently of the aggregation kernel. The theoretical observations of order of convergence is verified using the experimental order of convergence for analytically tractable kernels.