Application of the least-squares method for solving population balance problems in Rd+1

In multiphase chemical reactor analysis the prediction of the dispersed phase distribution plays a major role in achieving reasonable results. The combined CFD-PBE (population balance equations) are computationally intensive requiring efficient numerical methods for dealing with them. This paper presents the formulation and validation of a spectral least squares method for solving the steady state population balance equations in Rd+1, with d the physical spatial dimension and 1 the internal property dimension. The least-squares method consists in minimizing the integral of the square of the residual over the computational domain. Spectral convergence of the L-2-norm error of the solution and of the moments of the solution are verified for the zero- and one-dimensional cases using model problems with analytical solutions. (c) 2006 Elsevier Ltd. All rights reserved.