Convergence to Steady-States of Compressible Navier–Stokes–Maxwell Equations

2021 ◽  
Vol 32 (1) ◽  
Author(s):  
Yue-Hong Feng ◽  
Xin Li ◽  
Ming Mei ◽  
Shu Wang ◽  
Yang-Chen Cao
Keyword(s):  
Maxwell Equations ◽  
Steady States ◽  
Navier Stokes ◽  
Convergence To Steady States

scholarly journals A Derivation of Proca Equations on Cantor Sets: A Local Fractional Approach

2014 ◽  
Vol 10 ◽  
pp. 48-56 ◽  
Author(s):  
Victor Christianto ◽  
Biruduganti Rahul
Keyword(s):  
Maxwell Equations ◽  
High Energy Physics ◽  
Stokes Equations ◽  
High Energy ◽  
Cantor Sets ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fractal Media ◽  
Vector Calculus ◽  
Proca Equations

In a recent paper published at Advances in High Energy Physics (AHEP) journal, Yang Zhao et al. derived Maxwell equations on Cantor sets from the local fractional vector calculus. It can be shown that Maxwell equations on Cantor sets in a fractal bounded domain give efficiency and accuracy for describing the fractal electric and magnetic fields. Using the same approach, elsewhere Yang, Baleanu & Tenreiro Machado derived systems of Navier-Stokes equations on Cantor sets. However, so far there is no derivation of Proca equations on Cantor sets. Therefore, in this paper we present for the first time a derivation of Proca equations and GravitoElectroMagnetic (GEM) Proca-type equations on Cantor sets. Considering that Proca equations may be used to explain electromagnetic effects in superconductor, We suggest that Proca equations on Cantor sets can describe electromagnetic of fractal superconductors; besides GEM Proca-type equations on Cantor sets may be used to explain some gravitoelectromagnetic effects of superconductor for fractal media. It is hoped that this paper may stimulate further investigations and experiments in particular for fractal superconductor. It may be expected to have some impact to fractal cosmology modeling too.

Numerical Simulation of Electromagnetic Stirring Effect on Flow Pattern of Metal Melt

2011 ◽  
Vol 264-265 ◽  
pp. 1574-1579
Author(s):  
H. Namaki ◽  
S. Hossein Seyedein ◽  
M.R. Afshar Moghadam ◽  
R. Ghasemzadeh
Keyword(s):  
Flow Pattern ◽  
Maxwell Equations ◽  
Flow Model ◽  
Stokes Equations ◽  
Electromagnetic Stirring ◽  
Navier Stokes ◽  
Simultaneous Solution ◽  
Navier Stokes Equations ◽  
Stirring Effect ◽  
Good Agreement

In this study, a mathematical model was developed to simulate 2-D axisymmetric melt flow under magnetic field in a cylindrical container. The modeling of this process required the simultaneous solution of the turbulent Navier-Stokes equations together with Maxwell equations. The flow pattern in liquid bath was obtained using a two-equation κ-є turbulent flow model, which was further used to obtain the solute distribution. The governing differential equations were solved numerically using finite volume based finite difference method. The computed results, were found to be in good agreement with the measurements reported in the literature. The effect of stirring parameters on temperature homogeneity of the melt have been discussed and presented.

An AUSM-based Algorithm for Solving the Coupled Navier-Stokes and Maxwell Equations

2013 ◽  
Author(s):  
Richard J. Thompson ◽  
Andrew Wilson ◽  
Trevor M. Moeller ◽  
Charles Merkle
Keyword(s):  
Maxwell Equations ◽  
Navier Stokes

Reducing Convection Effects in Solidification by Applying Magnetic Fields Having Optimized Intensity Distribution

2003 ◽  
Author(s):  
Marcelo J. Colac¸o ◽  
George S. Dulikravich ◽  
Thomas J. Martin
Keyword(s):  
Sequential Quadratic Programming ◽  
Maxwell Equations ◽  
Numerical Procedure ◽  
Hybrid Optimization ◽  
Navier Stokes ◽  
B Splines ◽  
Hybrid Optimization Algorithm ◽  
Volume Method ◽  
Quasi Newton ◽  
Gravity Direction

This paper presents a numerical procedure for achieving desired features of a melt undergoing solidification by applying an external magnetic field whose intensity and spatial distribution are obtained by the use of a hybrid optimization algorithm. The intensities of the magnets along the boundaries of the container are described as B-splines. The inverse problem is then formulated as to find the magnetic boundary conditions (the coefficients of the B-splines) in such a way that the gradients of temperature along the gravity direction are minimized. For this task, a hybrid optimization code was used that incorporates several of the most popular optimization modules; the Davidon-Fletcher-Powell (DFP) gradient method, a genetic algorithm (GA), the Nelder-Mead (NM) simplex method, quasi-Newton algorithm of Pshenichny-Danilin (LM), differential evolution (DE), and sequential quadratic programming (SQP). Transient Navier-Stokes and Maxwell equations were discretized using finite volume method in a generalized curvilinear non-orthogonal coordinate system. For the phase change problems, an enthalpy formulation was used. The code was validated against analytical and numerical benchmark results with very good agreements in both cases.

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