Araştırma Makalesi

- 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.

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.

Finite difference method, High-resolution scheme, Flux limiter

- 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.

Birincil Dil | İngilizce |
---|---|

Konular | Mühendislik |

Bölüm | Research Articles |

Yazarlar | |

Erken Görünüm Tarihi | 30 Haziran 2022 |

Yayımlanma Tarihi | 30 Haziran 2022 |

Başvuru Tarihi | 15 Şubat 2022 |

Kabul Tarihi | 25 Mayıs 2022 |

Yayınlandığı Sayı | Yıl 2022, Cilt 1, Sayı 1 |

Bibtex | @araştırma makalesi { inotech1074319, journal = {Inspiring Technologies and Innovations}, address = {Kuzeykent Mahallesi Org. Atilla ATEŞ Paşa Caddesi Kastamonu Üniversitesi Mühendislik ve Mimarlık Fakültesi PK: 37150 Merkez/KASTAMONU}, publisher = {Kastamonu Üniversitesi}, year = {2022}, volume = {1}, number = {1}, pages = {1 - 8}, title = {Numerical Simulation of Convection-Diffusion Equation Using a Novel Flux Limiter}, key = {cite}, author = {Ünal, Osman} } |

APA | Ünal, O. (2022). Numerical Simulation of Convection-Diffusion Equation Using a Novel Flux Limiter . Inspiring Technologies and Innovations , 1 (1) , 1-8 . Retrieved from https://dergipark.org.tr/tr/pub/inotech/issue/70702/1074319 |

MLA | Ünal, O. "Numerical Simulation of Convection-Diffusion Equation Using a Novel Flux Limiter" . Inspiring Technologies and Innovations 1 (2022 ): 1-8 <https://dergipark.org.tr/tr/pub/inotech/issue/70702/1074319> |

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

RIS | TY - JOUR T1 - Numerical Simulation of Convection-Diffusion Equation Using a Novel Flux Limiter AU - OsmanÜnal Y1 - 2022 PY - 2022 N1 - DO - T2 - Inspiring Technologies and Innovations JF - Journal JO - JOR SP - 1 EP - 8 VL - 1 IS - 1 SN - - M3 - UR - Y2 - 2022 ER - |

EndNote | %0 Inspiring Technologies and Innovations Numerical Simulation of Convection-Diffusion Equation Using a Novel Flux Limiter %A Osman Ünal %T Numerical Simulation of Convection-Diffusion Equation Using a Novel Flux Limiter %D 2022 %J Inspiring Technologies and Innovations %P - %V 1 %N 1 %R %U |

ISNAD | Ünal, Osman . "Numerical Simulation of Convection-Diffusion Equation Using a Novel Flux Limiter". Inspiring Technologies and Innovations 1 / 1 (Haziran 2022): 1-8 . |

AMA | Ünal O. Numerical Simulation of Convection-Diffusion Equation Using a Novel Flux Limiter. INOTECH. 2022; 1(1): 1-8. |

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

IEEE |
O. Ünal
,
"Numerical Simulation of Convection-Diffusion Equation Using a Novel Flux Limiter",
Inspiring Technologies and Innovations,
c. 1,
sayı. 1,
ss.
1-8, Haz. 2022 |