Population Balance is a prominent ingredient of modeling transport phenomena. Population Balance Equations (PBEs) are coupled to Computational Fluid Dynamics (CFD) to simulate turbulent dispersed flows. One of the arising challenges is to obtain an appropriate discretization technique for the internal coordinate of PBEs, so the resulting equations can lead to acceptable solutions with affordabl...

Few tools exist for creating and visualizing complex three-dimensional simulation meshes, and these have limitations that restrict their application to particular geometries and circumstances. Mesh generation needs to trend toward ever more general applications. To that end, we have developed MeshVoro, a tool that is based on the Voro++ (Rycroft 2009) library and is capable of generating comple...

We review some fast and accurate numerical techniques for solving elliptic equations in complicated domains developed by the author and his colleagues in recent past. These are based on a combination of fast algorithms for regular domains and various domain embedding techniques. The fast algorithms for regular domains are derived from analysis of integral equation approach for solving elliptic ...

A method is developed for incorporating diffusion of chemicals in complex geometries into stochastic chemical kinetics simulations. Systems are modeled using the reaction-diffusion master equation, with jump rates for diffusive motion between mesh cells calculated from the discretization weights of an embedded boundary method. Since diffusive jumps between cells are treated as first order react...

We demonstrate the relevance of saddle-splay elasticity in nematic liquid crystalline fluids in the context of complex surface anchoring conditions and the complex geometrical confinement. Specifically, nematic cells with patterns of surface anchoring and colloidal knots are shown as examples where saddle-splay free energy contribution can have a notable role which originates from nonhomogeneou...

Glossary Numerical methods Processes in nature are often described by partial differential equations. Finding solutions to those equations is at the heart of many studies aiming at the explanation of observed data. Simulations of realistic physical processes requires generally the use of numerical methods – a special branch of applied mathematics – that approximate the partial differential equa...

The primary requirement for a mesh generator used in an automated tool is robustness. Surface based meshing algorithms fail very often especially with invalid boundary representation geometries. With generic boundary representation formats like STEP or IGES, invalid geometries are very common due to the loss of information and precision in CAD Data Exchange. This paper presents an approach to a...

We discuss the development of a numerical algorithm, and solver capable of performing large-eddy simulation in the very complex geometries often encountered in industrial applications. The algorithm is developed for unstructured hybrid grids, is non-dissipative, yet robust at high Reynolds numbers on highly skewed grids. Simulation results for a variety of flows are presented. 2003 Elsevier Inc...