A new framework for numerical modeling of population balance equations: Solving for the inverse cumulative distribution function. (21st September 2022) - Peterson, Joseph D.; Bagkeris, Ioannis; Michael, Vipin
Graphical abstract: Highlights: Efficient numerical methods are needed when solving population balance equations. Existing methods have limitations, including possible convergence to a wrong solution. A new method of handling PBEs is given, solving for the inverse CDF. We validate this method for binary fragmentation calculations Abstract: Population balance equations (PBE) are a class of integro-partial differential equations with applications spanning a broad range of engineering disciplines. When the state of a population (e.g. droplet size distribution) dictates the mechanical properties of its transporting fluid, modeling tools for solving PBEs must provide good accuracy at very low computational cost. The quadrature method of moments scheme (QMOM) is a popular numerical strategy for many applications, but it has a number of significant weaknesses including the possibility of converging to an incorrect solution. Motivated by limitations of QMOM, this paper introduces a new numerical framework, miCDF, in which standard PBE equations are transformed to solve for the inverse cumulative distribution function. This transformation is straightforward, making use of the triple product rule, and it can be implemented using simple finite difference methods. Through sample calculations, we discuss the advantages and limitations of miCDF relative to QMOM.