scholarly journals Coupling of the Flux Diffusion Equation with the Equilibrium Reconstruction at ASDEX Upgrade

2016 ◽  
Vol 69 (2) ◽  
pp. 526-536 ◽  
Author(s):  
R. Fischer ◽  
A. Bock ◽  
M. Dunne ◽  
J. C. Fuchs ◽  
L. Giannone ◽  
...  
Keyword(s):  
Diffusion Equation ◽  
Equilibrium Reconstruction ◽  
Flux Diffusion

scholarly journals The Dirichlet problem of a conformable advection-diffusion equation

2017 ◽  
Vol 21 (1 Part A) ◽  
pp. 9-18 ◽  
Author(s):  
Derya Avci ◽  
Eroğlu İskender ◽  
Necati Özdemir
Keyword(s):  
Dirichlet Problem ◽  
Diffusion Equation ◽  
Diffusion Processes ◽  
Fractional Power ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Local Fractional Calculus ◽  
Fractional Models ◽  
Matter Flux ◽  
Flux Diffusion

The fractional advection-diffusion equations are obtained from a fractional power law for the matter flux. Diffusion processes in special types of porous media which has fractal geometry can be modelled accurately by using these equations. However, the existing nonlocal fractional derivatives seem complicated and also lose some basic properties satisfied by usual derivatives. For these reasons, local fractional calculus has recently been emerged to simplify the complexities of fractional models defined by nonlocal fractional operators. In this work, the conformable, a local, well-behaved and limit-based definition, is used to obtain a local generalized form of advection-diffusion equation. In addition, this study is devoted to give a local generalized description to the combination of diffusive flux governed by Fick?s law and the advection flux associated with the velocity field. As a result, the constitutive conformable advection-diffusion equation can be easily achieved. A Dirichlet problem for conformable advection-diffusion equation is derived by applying fractional Laplace transform with respect to time t and finite sin-Fourier transform with respect to spatial coordinate x. Two illustrative examples are presented to show the behaviours of this new local generalized model. The dependence of the solution on the fractional order of conformable derivative and the changing values of problem parameters are validated using graphics held by MATLcodes.

PARTIAL HOMOGENIZATION OF THE DIFFUSION EQUATION WITH A DIRAC-LIKE POTENTIAL

2020 ◽  
Vol 18 (5) ◽  
pp. 507-518
Author(s):  
Latifa Ait Mahiout ◽  
Gregory P. Panasenko ◽  
Vitaly Volpert
Keyword(s):  
Diffusion Equation
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