A High-Accuracy Finite Difference Scheme for Solving Reaction-Convection-Diffusion Problems with a Small Diffusivity
Year: 2014
Author: Po-Wen Hsieh, Suh-Yuh Yang, Cheng-Shu You
Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 5 : pp. 637–662
Abstract
This paper is devoted to a new high-accuracy finite difference scheme for solving reaction-convection-diffusion problems with a small diffusivity $\varepsilon$. With a novel treatment for the reaction term, we first derive a difference scheme of accuracy $\mathcal{O}(\varepsilon^2 h + \varepsilon h^2 + h^3)$ for the 1-D case. Using the alternating direction technique, we then extend the scheme to the 2-D case on a nine-point stencil. We apply the high-accuracy finite difference scheme to solve the 2-D steady incompressible Navier-Stokes equations in the stream function-vorticity formulation. Numerical examples are given to illustrate the effectiveness of the proposed difference scheme. Comparisons made with some high-order compact difference schemes show that the newly proposed scheme can achieve good accuracy with better stability.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2014.5.s4
Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 5 : pp. 637–662
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Reaction-convection-diffusion equation incompressible Navier-Stokes equations boundary layer interior layer finite difference scheme.
Author Details
-
High-Order Compact Difference Method for Solving Two- and Three-Dimensional Unsteady Convection Diffusion Reaction Equations
Wei, Jianying | Ge, Yongbin | Wang, YanAxioms, Vol. 11 (2022), Iss. 3 P.111
https://doi.org/10.3390/axioms11030111 [Citations: 0] -
Adaptive High-Order Finite Difference Analysis of 2D Quenching-Type Convection-Reaction-Diffusion Equation
Zhu, Xiaoliang | Ge, Yongbin | Shmarev, SergeyAdvances in Mathematical Physics, Vol. 2020 (2020), Iss. P.1
https://doi.org/10.1155/2020/3650703 [Citations: 0] -
Calculation Method for the Early Warning Index of Sudden Water Pollution Based on the Linear Variation Assumption of the Substance Concentration in the River Network
Li, Dayong | Dong, Zengchuan | Wang, Chuanhai | Liu, Jintao | Yao, HongyiWater Resources Management, Vol. 34 (2020), Iss. 9 P.2821
https://doi.org/10.1007/s11269-020-02584-7 [Citations: 4] -
Quantitative study on the early warning indexes of conventional sudden water pollution in a plain river network
Li, Dayong | Wei, Yiming | Dong, Zengchuan | Wang, Chuanhai | Wang, CongcongJournal of Cleaner Production, Vol. 303 (2021), Iss. P.127067
https://doi.org/10.1016/j.jclepro.2021.127067 [Citations: 12] -
A Novel Technique for Constructing Difference Schemes for Systems of Singularly Perturbed Equations
Hsieh, Po-Wen | Shih, Yin-Tzer | Yang, Suh-Yuh | You, Cheng-ShuCommunications in Computational Physics, Vol. 19 (2016), Iss. 5 P.1287
https://doi.org/10.4208/cicp.scpde14.21s [Citations: 3]