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A Meshless Simulations for 2D Nonlinear Reaction-diffusion Brusselator System

Ahmad Shirzadi1, Vladimir Sladek2, Jan Sladek3

Department of Mathematics, Persian Gulf University, Bushehr, Iran. Email: shirzadi@pgu.ac.ir, shirzadi.a@gmail.com
Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia. Email: vladimir.sladek@savba.sk
Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia. Email: jan.sladek@savba.sk

Computer Modeling in Engineering & Sciences 2013, 95(4), 259-282. https://doi.org/10.3970/cmes.2013.095.259

Abstract

This paper is concerned with the development of a numerical approach based on the Meshless Local Petrov-Galerkin (MLPG) method for the approximate solutions of the two dimensional nonlinear reaction-diffusion Brusselator systems. The method uses finite differences for discretizing the time variable and the moving least squares (MLS) approximation for field variables. The application of the weak formulation with the Heaviside type test functions supported on local subdomains (around the nodes used in MLS approximation) to semi-discretized partial differential equations yields the finite-volume local weak formulation. A predictor-corrector scheme is used to handle the nonlinearity of the problem within each time step. Numerical test problems are given to verify the accuracy of the proposed method. Under particular conditions, this system exhibits Turing instability which results in a pattern forming instability. This concept is studied and a test problem is given.

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APA Style
Shirzadi, A., Sladek, V., Sladek, J. (2013). A meshless simulations for 2D nonlinear reaction-diffusion brusselator system. Computer Modeling in Engineering & Sciences, 95(4), 259-282. https://doi.org/10.3970/cmes.2013.095.259
Vancouver Style
Shirzadi A, Sladek V, Sladek J. A meshless simulations for 2D nonlinear reaction-diffusion brusselator system. Comput Model Eng Sci. 2013;95(4):259-282 https://doi.org/10.3970/cmes.2013.095.259
IEEE Style
A. Shirzadi, V. Sladek, and J. Sladek, “A Meshless Simulations for 2D Nonlinear Reaction-diffusion Brusselator System,” Comput. Model. Eng. Sci., vol. 95, no. 4, pp. 259-282, 2013. https://doi.org/10.3970/cmes.2013.095.259



cc Copyright © 2013 The Author(s). Published by Tech Science Press.
This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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