Abstract
To develop an efficient numerical scheme for three-dimensional advection diffusion equation, higher order ADI method was proposed. 2nd and fourth order ADI schemes were used to handle such problem. Von Neumann stability analysis shows that Alternating Direction Implicit scheme is unconditionally stable. The accuracy and efficiency of such schemes was depicted by two test problems. Numerical results for two test problems were carried out to establish the performance of the given method and to compare it with the others Typical methods. Fourth order ADI method were found to be very efficient and stable for solving three dimensional Advection Diffusion Equation. The proposed methods can be implemented for solving non-linear problems arising in engineering and physics.
Highlights
In this paper we are dealing with 3-D advection-diffusion equation
We found that earlier work done on[30] advection -diffusion equation in one and two dimensions using various finite difference schemes
In this research paper a numerical treatment for three dimensional advection-diffusion equation was discussed by means of Alternating Direction Implicit scheme
Summary
In this paper we are dealing with 3-D advection-diffusion equation. Many mathematical models non-linear differential equations plays a very important role in various physical biological and chemical phenomena.[1] Advection-diffusion equation have been applied in many areas of science and engineering, including economics, fluid dynamics, forecasting, astrophysics, oceanography, meteorology, etc.[2,3] To make a mathematical model of physical phenomena, it is essential to understand the behavior of equation. Advection-diffusion problems have a key role in computational fluid dynamics to simulate flow problems.[1,3,4,5] Development of such new proposed schemes with accurate stable and efficient results of advection-diffusion equation is of dynamic importance. 3-D advection-diffusion equation is given by the following equation.[6] ut + ξxux + ξyuy + ξzuz = ηxuxx + ηyuyy + ηzuzz (1)
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