by Qamar, S., Warnecke, G..
Series: 2006-28, Preprints
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.
Population balance model, aggregation, discretization, finite volume method.