Numerical Analysis of Convection–Diffusion Using a Modified Upwind Approach in the Finite Volume Method

Arafat Hussain, Zhoushun Zheng and Eyaya Fekadie Anley
Additional contact information
Arafat Hussain: School of Mathematics and Statistics, Central South University, Changsha 410083, China
Zhoushun Zheng: School of Mathematics and Statistics, Central South University, Changsha 410083, China
Eyaya Fekadie Anley: School of Mathematics and Statistics, Central South University, Changsha 410083, China

Mathematics, 2020, vol. 8, issue 11, 1-21

Abstract: The main focus of this study was to develop a numerical scheme with new expressions for interface flux approximations based on the upwind approach in the finite volume method. Our new proposed numerical scheme is unconditionally stable with second-order accuracy in both space and time. The method is based on the second-order formulation for the temporal approximation, and an upwind approach of the finite volume method is used for spatial interface approximation. Some numerical experiments have been conducted to illustrate the performance of the new numerical scheme for a convection–diffusion problem. For the phenomena of convection dominance and diffusion dominance, we developed a comparative study of this new upwind finite volume method with an existing upwind form and central difference scheme of the finite volume method. The modified numerical scheme shows highly accurate results as compared to both numerical schemes.

Keywords: finite volume method; second-order; convection–diffusion problem; stability; convergence order (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/11/1869/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/11/1869/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:11:p:1869-:d:436053

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().