Abstract
In this paper, we use the Adomian decomposition method (ADM), the finite differences method and the Alternating Direction Implicit method to estimate the advantages and the weakness of the above methods. For it, we make a numerical simulation of the different solutions constructed with these methods and compare the error investigated case.
Highlights
Http://creativecommons.org/licenses/by/4.0/ The advection-diffusion-reaction equation is a combination of the advection, Open Access diffusion and reaction equation
It describes physical phenomena, where the energy of the particles or other physical sizes is transferred in a physical system because of three processes: advection, diffusion and reaction
We got the exact solution, using the Adomian decomposition method (ADM) and the comparison has been done with the numerical solution obtained by ADI method
Summary
Http://creativecommons.org/licenses/by/4.0/ The advection-diffusion-reaction equation is a combination of the advection, Open Access diffusion and reaction equation. It describes physical phenomena, where the energy of the particles or other physical sizes is transferred in a physical system because of three processes: advection, diffusion and reaction. According to this definition, it follows that the equation of advection-diffusion contains a parabolic part (diffusion) and hyperbolic part (advection). In the case of constant coefficient of diffusion and constant rate of flow, the equation in 1D can be written in the following form:. The equations of advection-diffusion-reaction are used to describe the problems of transport (the transport of pollutants, flows in the conduits, the modeling of the air pollution, etc.) [1] [2] [3]
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