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2006-28

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

by Qamar, S., Warnecke, G..


Series: 2006-28, Preprints

MSC:
65M99 None of the above, but in this section
35L60 Nonlinear first-order hyperbolic equations
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.