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.

Comparison of Finite Difference and Finite Volume Method for Numerical Simulation of the Incompressible Viscous Driven Cavity Flow

2013 ◽  
Vol 732-733 ◽  
pp. 413-416
Author(s):  
Jian Wang ◽  
Jiang Fei Li ◽  
Wen Xue Cheng ◽  
Lian Yuan ◽  
Bo Li ◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Difference Method ◽  
Cavity Flow ◽  
Second Order ◽  
Central Difference ◽  
Driven Cavity ◽  
Volume Method

In this paper, finite difference method and finite volume method are applied to incompressible viscous driven cavity flow problems, and their results are analyzed and compared. As for the finite difference method, second-order upwind and second-order central difference format are applied to the discretization of the convection and diffusion items respectively. For the finite volume method, three different ways are utilized to discretize the control equations: QUICK, second-order central difference and third-order upwind formats. The results show that computing time as well as calculation accuracy exponentially depends on Reynolds number, discrete formats and grid numbers.

A CELL-CENTERED SECOND-ORDER ACCURATE FINITE VOLUME METHOD FOR CONVECTION–DIFFUSION PROBLEMS ON UNSTRUCTURED MESHES

2004 ◽  
Vol 14 (08) ◽  
pp. 1235-1260 ◽  
Author(s):  
ENRICO BERTOLAZZI ◽  
GIANMARCO MANZINI
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Second Order ◽  
Convection Diffusion ◽  
Slope Limiter ◽  
A Cell ◽  
Discrete Problems ◽  
Definition Of ◽  
Volume Method ◽  
Theoretical Issues

A MUSCL-like cell-centered finite volume method is proposed to approximate the solution of multi-dimensional steady advection–diffusion equations. The second-order accuracy is provided by an appropriate definition of the diffusive and advective numerical fluxes. The method is based on a least squares reconstruction of the vertex values from cell averages. The slope limiter, which is required to prevent the formation and growth of spurious numerical oscillations, is designed to guarantee that the discrete solution of the nonlinear scheme exists. Several theoretical issues regarding the solvability of the resulting discrete problems are thoroughly discussed. Finally, numerical experiments that validate the effectiveness of the approach are presented.

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