Mathematical and Computer Modelling of Dynamical Systems (Dec 2023)

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

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

DOI
https://doi.org/10.1080/13873954.2023.2282974
Journal volume & issue
Vol. 29, no. 1
pp. 265 – 285

Abstract

Read online

ABSTRACTDue 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.

Keywords