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Numerical Simulation of Convection-Diffusion Equation Using a Novel Flux Limiter

Year 2022, Volume: 1 Issue: 1, 1 - 8, 30.06.2022

Abstract

CFD (Computational Fluid Dynamics) researchers encounter some substantial problems such as numerical dispersion and unphysical oscillation. The first order space discretization technique causes to large numerical dispersion and it leads to inaccurate prediction of the flow behavior of fluids. Therefore, numerical simulation engineers apply some high-resolution schemes for instance QUICK (Quadratic Upstream Interpolation for Convective Kinematics) and TCDF (Third-order Continuously Differentiable Function) to reduce the impacts of the numerical dispersion. However, the higher order methods lead to undesirable and unphysical oscillations at large Courant number. First objective of this study is to propose a novel flux limiter obtained by modifying TCDF. The modified TCDF flux limiter function works at large Courant number without any unphysical oscillation contrary to the previously improved TCDF flux limiter. Second purpose of this study is to present a numerical simulator for solution of convection-diffusion equation. The Matlab codes and Google drive links related to this numerical simulator were added to Appendix to make other researchers’ works easy.

References

  • Wolcott, D. S., Kazemi, H., & Dean, R. H. (1996, October). A practical method for minimizing the grid orientation effect in reservoir simulation. In SPE annual technical conference and exhibition. OnePetro.
  • Leonard, B. P. (1979). A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Computer methods in applied mechanics and engineering, 19(1), 59-98.
  • Zhang, D., Jiang, C., Liang, D., & Cheng, L. (2015). A review on TVD schemes and a refined flux-limiter for steady-state calculations. Journal of Computational Physics, 302, 114-154.
  • Peaceman, D. W. (2000). Fundamentals of numerical reservoir simulation. Elsevier.
  • Ertekin, T., Abou-Kassem, J. H., & King, G. R. (2001). Basic applied reservoir simulation (Vol. 7). Richardson, TX: Society of Petroleum Engineers.
  • Liu, J. (1993). High-resolution methods for enhanced oil recovery simulation (Doctoral dissertation, The University of Texas at Austin).
  • Harten, A. (1984). On a class of high resolution total variation stable finite difference schemes. SIAM Journal on Numerical Analysis, 21(1), 1-23.
  • Sweby, P. K. (1984). High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM journal on numerical analysis, 21(5), 995-1011.
Year 2022, Volume: 1 Issue: 1, 1 - 8, 30.06.2022

Abstract

References

  • Wolcott, D. S., Kazemi, H., & Dean, R. H. (1996, October). A practical method for minimizing the grid orientation effect in reservoir simulation. In SPE annual technical conference and exhibition. OnePetro.
  • Leonard, B. P. (1979). A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Computer methods in applied mechanics and engineering, 19(1), 59-98.
  • Zhang, D., Jiang, C., Liang, D., & Cheng, L. (2015). A review on TVD schemes and a refined flux-limiter for steady-state calculations. Journal of Computational Physics, 302, 114-154.
  • Peaceman, D. W. (2000). Fundamentals of numerical reservoir simulation. Elsevier.
  • Ertekin, T., Abou-Kassem, J. H., & King, G. R. (2001). Basic applied reservoir simulation (Vol. 7). Richardson, TX: Society of Petroleum Engineers.
  • Liu, J. (1993). High-resolution methods for enhanced oil recovery simulation (Doctoral dissertation, The University of Texas at Austin).
  • Harten, A. (1984). On a class of high resolution total variation stable finite difference schemes. SIAM Journal on Numerical Analysis, 21(1), 1-23.
  • Sweby, P. K. (1984). High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM journal on numerical analysis, 21(5), 995-1011.
There are 8 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Articles
Authors

Osman Ünal 0000-0003-1101-6561

Early Pub Date June 30, 2022
Publication Date June 30, 2022
Submission Date February 15, 2022
Published in Issue Year 2022 Volume: 1 Issue: 1

Cite

APA Ünal, O. (2022). Numerical Simulation of Convection-Diffusion Equation Using a Novel Flux Limiter. Inspiring Technologies and Innovations, 1(1), 1-8.

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