Time-property least-squares spectral method for population balance equations

In multiphase chemical reactor analysis the dispersed phase distribution plays a major role in obtaining reliable predictions. The population balance equation is a well established equation for describing the evolution of the dispersed phase. However, the numerical solution of this type of equations is computationally intensive. In this work, a time-property least squares spectral method is presented for solving the population balance equation including breakage and coalescence processes. In this problem, both property and time are coupled in the least squares minimization procedure. Spectral convergence of the L ² least squares functional and L ² error norms in time-property is verified using a smooth solution to the population balance equation.