hp-adaptive least squares spectral element method for population balance equations

Population Balance Equations (PBE) are encountered in numerous scientific and engineering disciplines. This equation describes complex processes where the accurate prediction of the dispersed phase plays a major role for the overall behavior of the system. The PBE is a nonlinear partial integro-differential equation which is computationally intensive. This paper discusses the application of an hp-adaptive refinement technique applied to a least squares spectral element formulation for solving population balance equations. The refinement is based on an estimate of the local Sobolev regularity index of the underlying solution by monitoring the decay rate of its Legendre expansion coefficients. The performance of the method is demonstrated numerically by using analytical test cases.