Solution of the Population Balance Equation by the Meshless Moving Particle Method (MMPM)

01.Jan.2018

​In this contribution we deal with a critical problem in the numerical modelling of the dispersed phase flow systems using population balances. To solve this problem, we derived a Meshless Moving Particle Method (MMPM) which is based on coupling information and function approximation theories to recover the complete particle size distribution in a grid free environment. The particles, which adapt their positions according to population integral properties, are allowed to propagate using a few number of ODEs. These particle positions are found exactly the same as those predicted by the Chebyshev-QMOM; however, without iterative eigenvalue calculations. The overall complexity of the method is O(N) where N is the number of moving particles. The MMPM is validated using many test cases with known analytical solutions including microbial cell dynamics in a constant abiotic environment. The sequence of the continuous approximations of the number concentration function is found to converge with an order O(1/Nc) with c > 1.

https://www.researchgate.net/publication/326185151_Solution_of_the_Population_Balance_Equation_by_the_Meshless_Moving_Particle_Method_MMPM​