Vector Flux

2017 ◽  
pp. 157-178
Keyword(s):  
Vector Flux

General finite-volume framework for saddle-point problems of various physics

2021 ◽  
Vol 36 (6) ◽  
pp. 359-379
Author(s):  
Kirill M. Terekhov
Keyword(s):  
Saddle Point ◽  
Finite Volume ◽  
Navier Stokes ◽  
Saddle Point Problems ◽  
Surface Integral ◽  
Matrix Coefficients ◽  
Gauss Theorem ◽  
Stability Issue ◽  
Incompressible Elasticity ◽  
Vector Flux

Abstract This article is dedicated to the general finite-volume framework used to discretize and solve saddle-point problems of various physics. The framework applies the Ostrogradsky–Gauss theorem to transform a divergent part of the partial differential equation into a surface integral, approximated by the summation of vector fluxes over interfaces. The interface vector fluxes are reconstructed using the harmonic averaging point concept resulting in the unique vector flux even in a heterogeneous anisotropic medium. The vector flux is modified with the consideration of eigenvalues in matrix coefficients at vector unknowns to address both the hyperbolic and saddle-point problems, causing nonphysical oscillations and an inf-sup stability issue. We apply the framework to several problems of various physics, namely incompressible elasticity problem, incompressible Navier–Stokes, Brinkman–Hazen–Dupuit–Darcy, Biot, and Maxwell equations and explain several nuances of the application. Finally, we test the framework on simple analytical solutions.

Geometrical vector flux sinks and ideal flux concentrators

1981 ◽  
Vol 71 (6) ◽  
pp. 777 ◽  
Author(s):  
Peretz Greenman
Keyword(s):  
Vector Flux

Geometrical vector flux and some new nonimaging concentrators

1979 ◽  
Vol 69 (4) ◽  
pp. 532 ◽  
Author(s):  
R. Winston ◽  
W. T. Welford
Keyword(s):  
Vector Flux

Error Estimates of H1-Galerkin Mixed Finite Element Methods for Nonlinear Parabolic Problem

2011 ◽  
Vol 267 ◽  
pp. 504-509
Author(s):  
Hai Tao Che
Keyword(s):  
Error Estimates ◽  
Parabolic Problem ◽  
Dimensional Space ◽  
Mixed Finite Element ◽  
Consistency Condition ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Nonlinear Parabolic Problem ◽  
Nonlinear Parabolic ◽  
Vector Flux

In this paper, H1-Galerkin mixed element method is proposed to simulate the nonlinear Parabolic problem. The problem is considered in one dimensional space. and optimal error estimates are also established. In particular, our methods can simultaneously approximate the scalar unknown and the vector flux effectively, without requiring the LBB consistency condition.

Calculation of the poynting vector flux through a partially screened dielectric sphere

1989 ◽  
Vol 32 (2) ◽  
pp. 160-166 ◽  
Author(s):  
S. S. Vinogradov ◽  
A. V. Sulima
Keyword(s):  
Poynting Vector ◽  
Dielectric Sphere ◽  
Vector Flux

Electrical resistivity

2004 ◽  
Author(s):  
Robert E. Newnham
Keyword(s):  
Electrical Resistivity ◽  
Second Law Of Thermodynamics ◽  
Reciprocal Relation ◽  
Nonequilibrium Phenomena ◽  
Linear Relationships ◽  
Polar Tensor ◽  
Higher Order Tensors ◽  
Current Flows ◽  
Tensor Property ◽  
Vector Flux

The next six chapters describe the transport phenomena associated with the flow of charge, heat, and matter. In each case there is a vector flux that is governed by a vector field. Linear relationships between flux and field include electrical resistivity (Chapter 17), thermal conductivity (Chapter 18), diffusion (Chapter 19), and thermoelectricity (Chapter 21). All are represented by second rank tensors similar to electric permittivity (Chapter 9), but the underlying physics is somewhat different. Transport properties are nonequilibrium phenomena governed by statistical mechanics and the concept of microscopic reversibility, rather than the second law of thermodynamics that applies to equilibrium properties such as specific heat, permittivity, and elasticity. Higher order tensors appear when the transport experiments are carried out in the presence of magnetic fields or mechanical stresses. Galvanomagnetic, thermomagnetic (Chapter 20), and piezoresistance effects (Chapter 22) require third- and fourth-rank tensors. When an electric field is applied to a conductor, an electric current flows through the sample. The field Ei (in V/m) is related to the current density Jj (in A/m2) through Ohm’s Law, where ρij is the electrical resistivity (in Ω m). In tensor form, . . . Ei = ρijJj . . . Ei and Jj are polar vectors (first rank polar tensors) and ρij is a second rank polar tensor property which follows Neumann’s law in the usual way. Sometimes it is more convenient to use the reciprocal relation involving the electrical conductivity σij : . . . Ji = σijEj . . . .

scholarly journals Space Vector Flux Weakening Control of PMSM Drivers

2018 ◽  
Vol 192 ◽  
pp. 012010
Author(s):  
Gentao Dong ◽  
Jianfei Yang ◽  
Xin Qiu ◽  
Xun Liu ◽  
Cao Wei
Keyword(s):  
Space Vector ◽  
Vector Flux ◽  
Flux Weakening Control ◽  
Flux Weakening
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