High accuracy time and space transform method for advection-diffusion equation in an unbounded domain

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.

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High-accuracy numerical scheme for solving the space-time fractional advection-diffusion equation with convergence analysis

Alexandria Engineering Journal ◽

10.1016/j.aej.2021.04.092 ◽

2021 ◽

Author(s):

Y. Esmaeelzade Aghdam ◽

H. Mesgarani ◽

G.M. Moremedi ◽

M. Khoshkhahtinat

Keyword(s):

Diffusion Equation ◽

Convergence Analysis ◽

Numerical Scheme ◽

High Accuracy ◽

Space Time ◽

Advection Diffusion Equation ◽

Advection Diffusion

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ANALYTICAL SOLUTION OF A NON - HOMOGENEOUS ONE - DIMENSIONAL ADVECTION DIFFUSION EQUATION WITH TEMPORALLY VARYING COEFFICIENTS .

June-2020 - International Journal of Engineering Sciences & Research Technology ◽

10.29121/ijesrt.v9.i12.2020.7 ◽

2020 ◽

Vol 9 (12) ◽

pp. 49-58

Keyword(s):

Analytical Solution ◽

Diffusion Equation ◽

Transform Method ◽

One Dimensional ◽

Varying Coefficients ◽

Advection Diffusion Equation ◽

Advection Diffusion ◽

Advection Term ◽

Constant Coefficients ◽

Instantaneous Point

Advection Diffusion Equation is a partial differential equation that describes the transport of pollutants in rivers. Its coefficients (dispersion and velocity) can be constant, dependent on space or time or both space and time. This study presents an analytical solution of a one dimensional non - homogeneous advection diffusion equation with temporally dependent coefficients, describing one dimensional pollutant transport in a section of a river. Temporal dependence is accounted for by considering a temporally dependent dispersion coefficient along an unsteady flow assuming that dispersion is proportional to the velocity. Transformations are used to convert the time dependent coefficients to constant coefficients and to eliminate the advection term. Analytical solution is obtained using Fourier transform method considering an instantaneous point source. Numerical results are presented. The findings show that concentration monotonically decreases with increasing distance and increasing time.

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