The Weighted Upwinding Finite Volume Method for the Convection Diffusion Problem on a Nonstandard Covolume Grid

2004 ◽  
Vol 1 (1) ◽  
pp. 180-194 ◽  
Author(s):  
Dong Liang ◽  
Weidong Zhao
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Diffusion Problem ◽  
Convection Diffusion ◽  
Volume Method

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

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1869
Author(s):  
Arafat Hussain ◽  
Zhoushun Zheng ◽  
Eyaya Fekadie Anley
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Numerical Scheme ◽  
Diffusion Problem ◽  
Second Order ◽  
Order Accuracy ◽  
Central Difference ◽  
Convection Diffusion ◽  
Volume Method ◽  
And Diffusion

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.

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