Evaluation of the 1-point quadrature approximation in QMOM for combined aerosol growth laws

This work examines the applicability of various assumptions in implementation of the quadrature method of moments (QMOM) for solving problems in aerosol science involving simultaneous nucleation, surface growth and coagulation. The problem of aerosol growth and coagulation in a box and the problem of vapor condensation in a nozzle are reworked using quadrature method of moments. QMOM uses Gaussian quadrature to evaluate integrals appearing in the moment equations and therefore does not require any assumptions on the form of the size distribution function, the growth laws and coagulation kernels. Results are compared with calculations which assume a lognormal size distribution. The conditions for which one, two and higher quadrature points can be used in the quadrature formula and the issues regarding the accuracy are considered for combined aerosol nucleation, growth and coagulation processes. Results show that for these problems, the simplest 1-point quadrature scheme gives accuracy comparable with the lognormal calculations while using two and higher point quadrature gives highly accurate results. Some difficulties associated with the QMOM are discussed and some insights are provided.