Solving Population Balance Equation for Two-Component Aggregation by a Finite Volume Scheme

by Qamar, S.; Warnecke, G.


Preprint series: 06-28, Preprints

65M99 None of the above but in this section
35L60 Nonlinear first-order PDE of hyperbolic type
35L65 Conservation laws
65L99 None of the above but in this section


Abstract: A conservative finite volume approach, originally proposed by Filbet and Laurencot (2004) 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 are then solved by using adaptive RK45 method which is based on the embedded Runge-Kutta methods of order four and five. Several numerical test cases for the one and two-components aggregation process are considered here. The numerical results are validated against available analytical solutions.

Keywords: Population balance model, aggregation, discretization, finite volume method.

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