Numerical solutions of a two-dimensional population balance equation for aggregation
AIChE Spring National Meeting - 5th World Congress on Particle Technology (2006)
Contribution to Conference
A new discretization for a two dimensional aggregation population balance equation is developed. The discretization is an extension of the cell average technique proposed by the authors (J. Kumar et al. 2006, Chem. Eng. Sci. 61, 3327-3342) for one dimensional aggregation problems. The scheme is based on an exact prediction of certain moments of the population. The formulation is quite simple to implement, computationally less expensive than previous approaches and highly accurate. Numerical diffusion is a common problem with many numerical methods while applied on coarse grids. The presented technique nearly eliminates numerical diffusion and predicts three moments of the population at high accuracy. This is achieved by taking the average of all newborn particles in a cell and then assigning them to neighboring cells according to the cell average and the distance to neighboring nodes. The technique may be implemented on any type of grid. The accuracy of the scheme has been analyzed by comparing analytical and numerical solutions of a test problem. The numerical results are in excellent agreement with the analytical results and show the ability to predict higher moments very precisely. Additionally, an extension of the proposed technique to higher dimensional problems has been discussed.