Numerical solution of a multi-dimensional batch crystallization model with fines dissolution

Application of Discontinuous Galerkin Scheme to Batch Crystallization Models

“…It can be observed that the DG scheme gives a better approximation of the solution compared to the Koren scheme. 14,27 Once again, the scheme shows better performance in resolving right discontinuities. The stiff nucleation at the left boundary, which produces a sharp peak and a second step profile, makes this problem much harder than the previous problems.…”

“…14,26 This HR-FVS was found to be more efficient and accurate compared to other flux-limiting schemes for solving batch crystallization models. 14,27 This article is arranged as follows. In section 2, the proposed discontinuous Galerkin method is derived for the batch crystallization model.…”

“…Besides different classes of schemes, DG schemes are more stable and high-order accurate, are capable of handling complex geometries and irregular meshes with hanging nodes, and can incorporate arbitrary degrees of polynomial approximations in different elements. , The test cases of this paper verify the accuracy and efficiency of the scheme for solving such models. For validation, the numerical results of the current scheme are compared with the flux-limiting high resolution finite volume scheme (HR-FVS) of Koren. , This HR-FVS was found to be more efficient and accurate compared to other flux-limiting schemes for solving batch crystallization models. , …”

The space time CE/SE method for solving one-dimensional batch crystallization model with fines dissolution

“…The dissolution of fines reduces undesirable small crystals and helps in achieving the desired CSD. Furthermore, it facilitates downstream processes such as filtration [2].…”

High Resolution Finite Volume Schemes for Solving Multivariable Biological Cell Population Balance Models

“…While analytical solutions are available for simplified cases only, researchers in this field started concentrating on the numerical techniques rather than finding the exact solutions. A number of numerical techniques are available for the solution of population balance equations (PBEs), such as methods of moments, , weighted residual method, method of characteristics, , Monte Carlo simulation, finite difference methods, , and high resolution finite volume schemes. , These numerical techniques were also extended to solve multivariable population balance models for different chemical engineering processes, such as crystallization, fluidized beds, and aerosol formation, and for predicting the interacting hydrodynamics and mass transfer in liquid–liquid extraction columns. − Moreover, the finite difference, finite element, and spectral methods were applied to solving multivariable cell population balance models. − …”