Solving population balance equations for two-component aggregation by a finite volume scheme

A conservative finite volume approach, originally proposed by Filbet and Laurençot [2004a. Numerical simulation of the Smoluchowski coagulation equation. SIAM Journal on Scientific Computing 25(6), 2004–2048] for the one-dimensional aggregation, is extended to simulate two-component aggregation. In order to apply the finite volume scheme, we reformulate the original integro-ordinary differential population balance equation for two-component aggregation problems into a partial differential equation of hyperbolic-type. Instead of using a fully discrete finite volume scheme and equidistant discretization of internal properties variables, we propose a semidiscrete upwind formulation and a geometric grid discretization of the internal variables. The resultant ordinary differential equations (ODEs) are then solved by using a standard adaptive ODEs-solver. Several numerical test cases for the one and two-components aggregation process are considered here. The numerical results are validated against available analytical solutions.