Application of the least-squares method for solving population balance problems in Rd+1Rd+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+1Rd+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 L2L2-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.