Systematic formulation of a general numerical framework for solving the two-dimensional convection–diffusion

Systematic formulation of a general numerical framework for solving the two-dimensional convection–diffusion–reaction system

Published:2020-11-12 Issue:7-8 Volume:22 Page:843-859
ISSN:1565-1339
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
language:en
Short-container-title:

Author:

V. Sugathan Aswin¹,Awasthi Ashish¹

Affiliation:

1. Department of Mathematics , National Institute of Technology , Calicut , 673601 , Kerala , India

Abstract

Abstract A general numerical framework is designed for the two-dimensional convection–diffusion–reaction (CDR) system. The compatibility of differential quadrature and finite difference methods (FDM) are utilized for the formulation. The idea is to switch one numerical scheme to another numerical scheme without changing the formulation. The only requirement is to input the weighting coefficients associated with the derivative discretizations to the general algorithm. Three numerical schemes comprising combinations of differential quadrature and FDMs are studied using the general algorithm. Properties of numerical schemes and the algorithm are analyzed by using the simulations of two-dimensional linear CDR system, Burgers’ equation, and Brusselator model.

Funder

Kerala State Council for Science, Technology and Environment

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modelling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ijnsns-2019-0231/pdf

Reference42 articles.

1. R. Eymard, D. Hilhorst, and M. Vohralík, “A combined finite volume–finite element scheme for the discretization of strongly nonlinear convection–diffusion–reaction problems on nonmatching grids,” Numer. Methods Part. Differ. Equ.: Int. J., vol. 26, no. 3, pp. 612–646, 2010, https://doi.org/10.1002/num.20449.

2. C. De Falco, R. Sacco, and M. Verri, “Analytical and numerical study of photocurrent transients in organic polymer solar cells,” Comput. Methods Appl. Mech. Eng., vol. 199, nos 25–28, pp. 1722–1732, 2010, https://doi.org/10.1016/j.cma.2010.01.018.

3. B. Luo, H-N. Wu, and H-X. Li, “Adaptive optimal control of highly dissipative nonlinear spatially distributed processes with neuro-dynamic programming,” IEEE Trans. Neural Network. Learn. Syst., vol. 26, no. 4, pp. 684–696, 2015, https://doi.org/10.1109/TNNLS.2014.2320744.

4. J. Karátson and B. Kovács, “A parallel numerical solution approach for nonlinear parabolic systems arising in air pollution transport problems,” in Mathematical Problems in Meteorological Modelling, Switzerland, Springer, 2016, pp. 57–70.

5. R. K. Sinha and J. Geiser, “Error estimates for finite volume element methods for convection–diffusion–reaction equations,” Appl. Numer. Math., vol. 57, no. 1, pp. 59–72, 2007, https://doi.org/10.1016/j.apnum.2005.12.002.