Numerical methods for solving two-dimensional aggregation population balance equations

Abstract

The cell average technique (CAT) and the fixed pivot (FP) method for solving two-dimensional aggregation population balance equations using a rectangular grid were implemented in Kumar et al. (2008). Recently, Chakraborty and Kumar (2007) have studied the FP scheme for the same problem on two different types of triangular grids and found that the method shows better results for number density as compared to the rectangular grids. However, they did not discuss the results for higher moments. Therefore, our first aim in this work is to compare different moments calculated by the FP technique on rectangular and triangular meshes with the analytical moments. Further we introduce a new mathematical formulation of the CAT for the two different types of triangular grids as considered by Chakraborty and Kumar (2007). The new formulation is simple to implement and gives better accuracy as compared to the rectangular grids. Three different test problems are considered to analyze the accuracy of both schemes by comparing the analytical and numerical solutions. The new formulation shows good agreement with the analytical results for number density and higher moments.