ACM Transactions on Mathematical Software (TOMS)
A Least-Squares Spectral Element Formulation for the Stokes Problem
Journal of Scientific Computing
Spectral/hp least-squares finite element formulation for the Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
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The combined CFD-PBM (population balance models) are computationally intensive, so a possibility is to calculate only a few moments of the probability density function (PDF) of the PBM minimizing the computational costs. However, this formulation results in an excess of unknowns with respect to equations which is referred to as a closure problem. One approach for dealing with this closure problem is to apply a numerical quadrature approximation. On the other hand, a different possibility is to compute the PDF and from this, the moments of interest if required.In this work, the two mentioned approaches are discussed and numerical experiments are used to show the capability of the methods for predicting the moments of the PBE. In particular, the quadrature method of moments and a time-space least squares spectral method will be discussed.