Quadratic upwind differencing scheme in the finite volume method for solving the convection-diffusion equation

Minilik Ayalew, Mulualem Aychluh, Daya Lal Suthar and Sunil Dutt Purohit

Mathematical and Computer Modelling of Dynamical Systems, 2023, vol. 29, issue 1, 265-285

Abstract: Due to the high importance of the convection-diffusion equation, we aim to develop a quadratic upwind differencing scheme in the finite volume approach for solving this equation. Our newly developed numerical approach is conditionally stable. The strategy employs a quadratic upwind differencing scheme in the finite volume technique for spatial approximation with third-order accuracy. The temporal integration is approximated using the explicit theta method of first-order accuracy. Some numerical examples are given to support our theoretical procedures. The findings are plotted using MATLAB R2016a mathematical software.

Date: 2023
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DOI: 10.1080/13873954.2023.2282974

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