Browsing by Author "Ganesan, Sashikumaar"
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- ItemA comparative study of a direct discretization and an operator-splitting solver for population balance systems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Anker, Felix; Ganesan, Sashikumaar; John, Volker; Schmeyer, EllenA direct discretization approach and an operator-splitting scheme are applied for the numerical simulation of a population balance system which models the synthesis of urea with a uni-variate population. The problem is formulated in axisymmetric form and the setup is chosen such that a steady state is reached. Both solvers are assessed with respect to the accuracy of the results, where experimental data are used for comparison, and the efficiency of the simulations. Depending on the goal of simulations, to track the evolution of the process accurately or to reach the steady state fast, recommendations for the choice of the solver are given.
- ItemAn operator-splitting heterogeneous finite element method for population balance equations: stability and convergence(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Ganesan, SashikumaarWe present a heterogeneous finite element approximation of the solution of a population balance equation, which depends both the physical and internal property coordinates. We employ the operator-splitting method to split the high-dimensional population balance equation into two low-dimensional equations, and discretize the low-dimensional equations separately. In particular, we discretize the physical and internal spaces with the standard Galerkin and Streamline Upwind Petrov Galerkin (SUPG) finite elements, respectively. It is demonstrated that the variational form of the operator-split population balance equation is equivalent to the variational form of the standard equation up to a perturbation term of order $tau^2$ in the backward Euler scheme, where $tau$ is a time step. Further, the stability and error estimates have been derived for the heterogeneous finite element discretization scheme applied to the population balance equation. It is shown that a slightly more regularity, $i.e,$ the mixed partial derivatives of the solution has to be bounded, is necessary for the solution of the population balance equation with the operator-splitting finite element method. Numerical results are presented to demonstrate the accuracy of the numerical scheme.