Computational solutions of three-dimensional advection-diffusion equation using fourth order time efficient alternating direction implicit scheme

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 sta...

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Bibliographic Details
Published in:AIP advances 2017-08, Vol.7 (8), p.085306-085306-13
Main Authors: Saqib, Muhammad, Hasnain, Shahid, Mashat, Daoud Suleiman
Format: Article
Language:English
Subjects:
Advection
Advection-diffusion equation
Alternating direction implicit methods
Diffusion
Dimensional stability
Stability analysis
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Summary: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.
ISSN:2158-3226
2158-3226
DOI:10.1063/1.4996341