The quadrature method of moments and its relationship with the method of weighted residuals

Population balance models are generally computationally intensive, so in many practical applications only a few moments of the density function are computed, minimizing the computational costs. Nevertheless, the moment formulation contains an excess of unknowns with respect to equations denoting a closure problem. One possible solution to this closure problem might be to apply a numerical quadrature approximation.In this work, the relationship between the quadrature approximation and the well-known method of weighted residuals (MWR) is discussed. An important result obtained in this work is that the problem of reconstruction of the density function is avoided using the MWR version of the quadrature approximation. Numerical experiments are performed in order to elucidate the advantages and disadvantages of the quadrature approximations.