Abstract
We investigate the application of the method of moments approach for the one-dimensional population balance equation. We consider different types of moment closures, including polynomial (PN) closures and minimum entropy (MN) closures. Additionally, we transfer the concept of Kershaw closures (KN) from radiative head transfer to the population balance equation. Realizability-preserving schemes for the moment closures as well as for a discontinuous Galerkin discretization of the space-dependent population balance equation are discussed. The numerical examples range from spatially homogeneous cases to a population balance equation coupled with the stationary incompressible Navier–Stokes equation. A detailed numerical discussion of accuracy, order of the moment method and computational time is given. We show that the minimum entropy closures are comparable or superior to the Kershaw closures in these test cases. In addition, we demonstrate that higher-order numerical schemes can be applied to the moment equations of the population balance equation.
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