Automatic Differentiation based QMOM for Population Balance Equations

The quadrature method of moments (QMOM) has emerged as a promising tool for the solution of population balance equations in the past few years. The QMOM requires solving differential algebraic equations (DAEs) consisting of ordinary differential equations related to the evolution of moments as well as nonlinear algebraic equations resulting from the quadrature approximation of moments. In this paper, the use of automatic differentiation (AD) technique is proposed for solution of DAEs arising in QMOM. In the proposed method, the variables of interest are approximated using high-order Taylor series. Using AD, the high-order Taylor coefficients can be recursively calculated to obtain high-fidelity solution of the DAE system. Benchmark examples drawn from literature are used to demonstrate the superior accuracy and computational advantage of the AD-QMOM over existing state-of-the-art techniques, such as DAE-QMOM.