Accurate and efficient solution of bivariate population balance equations using unstructured grids

In this work we demonstrate an application of the cell average technique (CAT) for solving bivariate population balance equations on unstructured triangular grids. Various strategies for improving unstructured grids are also discussed in this work. It is observed that the main unwanted feature of the triangular grid are elongated triangles. Strategies for removing such elements are suggested. It is shown that such an improvement reduces the number of pivots by 50% and leads to a drastic reduction of computational time without affecting the accuracy of the solution. Comparison of the numerical solution with the exact solution reveals that the cell average technique on unstructured triangular grid produces a better solution in comparison to the cell average technique on a structured triangular grid. It also produces better results in comparison to fixed pivot technique (FPT) on both structured triangular and unstructured triangular grids. In conclusion, the cell average technique with improved irregular triangular mesh can be seen as the smartest solution technique for the solution of bivariate population balance equations.