### 2006-28

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.