By Konstantin Volkov
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Extra info for Aerosols: Science and Case Studies
Ganesan. An operator‐splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence. ESAIM. Mathematical Modelling and Numerical Analysis, 46(6):1447–1465, 2012.  J. Solsvik and H. A. Jakobsen. Evaluation of weighted residual methods for the solution of a population balance model describing bubbly flows: the least‐squares, Galerkin, tau, and orthogonal collocation methods. Industrial and Engineering Chemistry Research, 52(45):15988–16013, 2013.  Y.
The new generalized TEMOM successfully overcomes the shortcomings of the old version whose 39 40 Aerosols - Science and Case Studies geometric standard deviation must be less than a certain value. In addition, the accuracy of numerical calculation for capturing fractional moments at an initial stage can be largely increased. In the generalized TEMOM, the closure function shown in Eq. (8) is changed, in which the moment sequence is composed not only by integer moments but also by fractional moments.
The TEMOM has been applied in many aerosol‐related problems and has also successfully been used for the realistic environmental and engineering problems where multidynamics are involved [71, 72]. However, all of these quoted studies were only taken into consideration for three‐order Taylor series expansion using integer moment sequence. The recent study shows that this kind of solution leads to shortcoming of the existing TEMOM, that is, the initial geometric standard deviation is limited, and the fractional moment at an initial stage cannot be accurately captured.