scholarly journals Fundamental Solutions to Time-Fractional Advection Diffusion Equation in a Case of Two Space Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Y. Z. Povstenko
Keyword(s):  
Diffusion Equation ◽  
Half Plane ◽  
Bessel Functions ◽  
Fourier Transforms ◽  
Integral Transform ◽  
Fundamental Solutions ◽  
Numerical Results ◽  
Dirichlet Problems ◽  
Advection Diffusion Equation ◽  
Advection Diffusion

The fundamental solutions to time-fractional advection diffusion equation in a plane and a half-plane are obtained using the Laplace integral transform with respect to timetand the Fourier transforms with respect to the space coordinatesxandy. The Cauchy, source, and Dirichlet problems are investigated. The solutions are expressed in terms of integrals of Bessel functions combined with Mittag-Leffler functions. Numerical results are illustrated graphically.

Analysis of advective–diffusive transport phenomena modelled via non-singular Mittag-Leffler kernel

2019 ◽  
Vol 14 (3) ◽  
pp. 309
Author(s):  
Derya Avci ◽  
Aylіn Yetіm
Keyword(s):  
Diffusion Equation ◽  
Fundamental Solutions ◽  
Diffusive Transport ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Main Motivation ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Fourier Transform Methods ◽  
Computational Processes

In this study, a linear advection–diffusion equation described by Atangana–Baleanu derivative with non-singular Mittag-Leffler kernel is considered. The Cauchy, Dirichlet and source problems are formulated on the half-line. The main motivation of this work is to find the fundamental solutions of prescribed problems. For this purpose, Laplace transform method with respect to time t and sine/cosine-Fourier transform methods with respect to spatial coordinate x are applied. It is remarkable that the obtained results are quite similar to the existing fundamental solutions of advection–diffusion equation with time-Caputo fractional derivative. Although the results are mathematically similar in both formulations, the AB derivative is a non-singular operator and provides a significant advantage in the computational processes. Therefore, it is preferable to replace the Caputo derivative in modelling such diffusive transports.

Space-Time and Motion to Advection-Diffusion Equation

2021 ◽  
Vol 3 (1) ◽  
pp. 34-43
Author(s):  
Mohammad Ghani
Keyword(s):  
Diffusion Equation ◽  
Space Time ◽  
Numerical Results ◽  
Smooth Functions ◽  
Equation Problem ◽  
Time Motion ◽  
Advection Diffusion Equation ◽  
Time And Motion ◽  
Advection Diffusion ◽  
Finite Differences Method

AbstractWe are concerned with the study the differential equation problem of space-time and motion for the case of advection-diffusion equation. We derive the advection-diffusion equation from the conservation of mass, where this can be represented by the substance flow in and flow out through the medium. In this case, the concentration of substance and rate of flow of substance in a medium are smooth functions which is useful to generate advection-diffusion equation. A special case of the advection-diffusion equation and numerical results are also given in this paper. We use explicit and implicit finite differences method for numerical results implemented in MATLAB.Keywords: advection-diffusion; space-time; motion; finite difference method. AbstrakKami tertarik untuk mempelajari masalah persamaan diferensial ruang-waktu, dan gerak untuk kasus persamaan adveksi-difusi. Kita menurunkan persamaan adveksi-difusi dari kekekalan massa, di mana hal ini dapat diwakili oleh aliran zat yang masuk dan keluar melalui media. Dalam hal ini konsentrasi zat dan laju aliran zat dalam suatu medium merupakan fungsi halus yang berguna untuk menghasilkan persamaan adveksi-difusi. Sebuah kasus khusus persamaan adveksi-difusi dan hasil numerik juga diberikan dalam makalah ini. Kami menggunakan metode beda hingga explisit dan implisit untuk hasil numerik yang diimplementasikan dalam MATLAB.Kata kunci: adveksi-difusi; ruang-waktu; gerak; metode beda hingga.

Fractional advection–diffusion equation with memory and Robin-type boundary condition

2019 ◽  
Vol 14 (3) ◽  
pp. 306 ◽  
Author(s):  
Itrat Abbas Mirza ◽  
Dumitru Vieru ◽  
Najma Ahmed
Keyword(s):  
Diffusion Equation ◽  
Fourier Transforms ◽  
Solute Concentration ◽  
Minimum Concentration ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Type Boundary ◽  
The One ◽  
Type Boundary Condition ◽  
With Memory

The one-dimensional fractional advection–diffusion equation with Robin-type boundary conditions is studied by using the Laplace and finite sine-cosine Fourier transforms. The mathematical model with memory is developed by employing the generalized Fick’s law with time-fractional Caputo derivative. The influence of the fractional parameter (the non-local effects) on the solute concentration is studied. It is found that solute concentration can be minimized by decreasing the memory parameter. Also, it is found that, at small values of time the ordinary model leads to minimum concentration, while at large values of the time the fractional model is recommended.

scholarly journals Simulation of three-dimensional transient pollutant dispersion in low wind conditions using the 3D-GILTT technique

2020 ◽  
Vol 5 (6) ◽  
Author(s):  
Viliam Cardoso Da Silveira ◽  
Daniela Buske ◽  
Régis Sperotto De Quadros
Keyword(s):  
Diffusion Equation ◽  
Integral Transform ◽  
Dispersion Model ◽  
Three Dimensional ◽  
Pollutant Dispersion ◽  
Transient Model ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Laplace Transform Technique ◽  
The Usa

The aim of this work is to present a transient model in low wind conditionsto simulate the pollutants dispersion in the atmosphere. The dispersion model is based in the advection-diffusion equation and it considers the zonal and meridional components of the wind. The transient advection-diffusion equation is solved using integral transform techniques. In this work, the generalized integral transform and Laplace techniques are used, known in the literature as GILTT and which applied to the three-dimensional problem is called 3D-GILTT (Three-dimensional Generalized Integral Laplace Transform Technique). To validate the model, data from INEL experiment (Idaho National Engineering Laboratory) carried out in the USA were used. The model simulates the observed concentrations in a satisfactory way and can be used for regulatory air quality applications

Sign in / Sign up

Export Citation Format

Share Document