Improving the accuracy of the moments method for solving the aerosol general dynamic equation

The General Dynamic Equation for aerosol evolution is converted into a set of ordinary differential equations for the moments Mm by multiplying by vm and integrating over particle volume, v. Closure of these equations is achieved by assuming a functional form for the moments, instead of the usual assumption of a functional form for the size distribution itself. Specifically, it is assumed that In(Mm) can be expressed as a pth-order polynomial in m. The time-dependent coefficients in the polynomial are found by solving (p + 1) differential equations numerically. The case p = 2 corresponds to the assumption that the size distribution is always log-normal but comparison with accurate solutions shows that increasing p increases the accuracy of the method for all processes considered (removal, condensation and Brownian coagulation). Particle loss during evaporation and achievement of a self-preserving form for Brownian coagulation are also considered. Inversion of the moment expression to obtain the size distribution using the Mellin inversion formula is discussed.