(315c) Accurate and Efficient Discrete Finite Volume Approximations for Population Balances Incorporating Coagulation and Fragmentation

This work is focused on developing two finite volume schemes for approximating the 1D and 2D simultaneous coagulation-fragmentation population balance equations. The two finite volume schemes are different in a sense that one scheme is merely focused on conserving the total mass of the system whereas the other scheme preserves the total number of particles as well as conserves the total mass of the system. Both schemes rely on introducing weights in their formulations to retain different properties such as total mass and total number of particles in the system. The inherit issue of the existing finite volume schemes is that it required very fine grid for predicting the number density function accurately (Kumar et al. 2009). In addition to this, the sectional methods such as fixed pivot technique and cell average technique are computationally very expensive due to their complex formulations although highly accurate. Moreover, solving a system involving simultaneous coagulation-fragmentation mechanisms rather add values to the computational cost. In order to overcome these issues, two finite volume schemes are developed and compared with the cell average technique along with newly developed exact solutions. The comparison reveals that both new finite volume schemes approximate the number density functions and their corresponding different order moments with higher accuracy even on a coarse grid at a lesser computational cost. It is also shown that considering fine grid for the approximation of numerical results lead to equal accuracy for cell average method and finite volume methods, however, both finite volume schemes are still computationally less expensive. Additionally, it is shown that both schemes can be easily extended to solve higher dimensional problems and retains the numerical accuracy and efficiency.

Keywords: Particle, Fragmentation, Coagulation, Population Balances, Finite volume Scheme, Cell Average Technique.