A finite element method for transmission in non-uniform ducts without flow: Comparison with the method of weighted residuals

Abstract A finite element method (FEM) based tool is used in this work to numerically modeling mineral-slurry like flows in a 3D lid-driven cavity. Accordingly, the context in which the referred FEM based tool is being developed is firstly emphasized. Both mathematical and numerical models utilized here are described next. A special emphasis is put on the flow governing equations and the particular FEM weighted residuals approach (Galerkin method) used to solve these equations. Since mineral-slurry flows both featuring relatively low flow velocities and containing large amounts of solid particles can be accounted for as laminar non-Newtonian flows, only laminar flows are discussed here. Indeed both Newtonian and non-Newtonian laminar flows are numerically studied using a 3D lid-driven cavity at two different Reynolds numbers. Two rheological models, power-law and Carreau-Yasuda, are utilized in the non-Newtonian flow simulations. When possible, the numerical results obtained here are compared with other numerical and experimental ones available in open literature. The associated averaged discrepancies from such comparisons are about 1%. The results obtained from the numerical simulations carried out here highlight the usefulness of the FEM based tool used in this work for realistically predicting the behavior of 3D Newtonian and non-Newtonian laminar flows. Multiphase turbulent flows including fluid-particle interaction models will be considered in future developments of this tool such to allow it properly representing the entire mineral-slurry transport phenomenon.

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An Integral Equation based Numerical Solution for Nanoparticles Illuminated with Collimated and Focused Light

MRS Proceedings ◽

10.1557/proc-1182-ee13-42 ◽

2009 ◽

Vol 1182 ◽

Author(s):

Kursat Sendur

Keyword(s):

Finite Element Method ◽

Integral Equation ◽

Finite Element ◽

Numerical Solution ◽

Surrounding Medium ◽

Solution Procedure ◽

Spherical Particles ◽

Field Equations ◽

Weighted Residuals ◽

Element Method

AbstractAn integral equation based numerical solution is developed when the particles are illuminated with collimated and focused incident beams. The solution procedure uses the method of weighted residuals, in which the integral equation is reduced to a matrix equation and then solved for the unknown electric field distribution. In the solution procedure, the effects of the surrounding medium and boundaries are taken into account using a Green’s function formulation. Therefore, there is no additional error due to artificial boundary conditions unlike differential equation based techniques, such as finite difference time domain and finite element method. In this formulation, only the scattering nano-particle is discretized. The results are compared to the analytical Mie series solution for spherical particles, as well as to the finite element method for rectangular metallic particles. The Richards-Wolf vector field equations are combined with the integral equation based formulation to model the interaction of nanoparticles with linearly and radially polarized incident focused beams.

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Simulation of tuning graphene plasmonic behaviors by ferroelectric domains for self-driven infrared photodetector applications

Nanoscale ◽

10.1039/c9nr06508c ◽

2019 ◽

Vol 11 (43) ◽

pp. 20868-20875 ◽

Cited By ~ 1

Author(s):

Junxiong Guo ◽

Yu Liu ◽

Yuan Lin ◽

Yu Tian ◽

Jinxing Zhang ◽

...

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Interfacial Effect ◽

Infrared Photodetector ◽

The Finite Element Method ◽

Ferroelectric Domains ◽

Element Method

We propose a graphene plasmonic infrared photodetector tuned by ferroelectric domains and investigate the interfacial effect using the finite element method.

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