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Journals / Karadeniz Fen Bilimleri Dergisi / 2022 / Cilt: 12 - Sayı: 2

An Innovative Approach for Numerical Solution of the Unsteady Convection-Dominated Flow Problems

Kararsız Konveksiyon Ağırlıklı Akış Problemlerinin Sayısal Çözümü için Yenilikçi bir Yaklaşım

Osman ÜNAL
Nuri AKKAŞ
Pages
1069–1080
Publication Date
2022-12-15
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, all Matlab codes of numerical and analytical solutions for convection-diffusion equation are added to Appendix in order to facilitate other researchers’ work.

📌 3 Key Takeaways

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Objective & Hypothesis:In this study, convection-diffusion equation is solved numerically using four different space discretization methods namely first-order upwinding, second-order central difference, cubic (partially upwinded) and cubic-TVD (Total Variation Diminishing) techniques.
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Key Findings & Data:Proposed model decreases numerical errors significantly compared to previously developed techniques.
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Conclusion & Impact:Finally, all Matlab codes of numerical and analytical solutions for convection-diffusion equation are added to Appendix in order to facilitate other researchers’ work.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Konveksiyon ağırlıklı akış · Sayısal dağılım · Fiziksel olmayan salınım

Abstract

In this study, convection-diffusion equation is solved numerically using four different space discretization methods namely first-order upwinding, second-order central difference, cubic (partially upwinded) and cubic-TVD (Total Variation Diminishing) techniques. All methods are compared with the analytical solution. The first-order method is not close to the analytical solution due to the numerical dispersion. The higher-order techniques reduce numerical dispersion. However, they cause another numerical error, unphysical oscillation. This study proposes an innovative approach on cubic-TVD method to eliminate undesired oscillations. Proposed model decreases numerical errors significantly compared to previously developed techniques. Moreover, numerical results of presented model quite close to the analytical solution. Finally, all Matlab codes of numerical and analytical solutions for convection-diffusion equation are added to Appendix in order to facilitate other researchers’ work.

Özet

Bu çalışmada, konveksiyon-difüzyon denklemi; birinci dereceden yukarı yelpaze, ikinci dereceden merkezi fark alma, kübik (kısmen yukarı yelpaze uygulanmış) ve kübik-TVD (Toplam Varyasyon Azaltma) teknikleri olmak üzere dört farklı uzay ayrıklaştırma yöntemi kullanılarak sayısal olarak çözülmüştür. Tüm yöntemler analitik çözümle karşılaştırılmıştır. Birinci dereceden yöntem, sayısal dağılım nedeniyle analitik çözüme yakın değildir. Daha yüksek mertebeden teknikler sayısal dağılımı azaltmaktadır, ancak bir diğer sayısal hataya, fiziksel olmayan salınımlara sebep olmaktadırlar. Bu çalışma, istenmeyen salınımları ortadan kaldırmak için kübik-TVD yöntemine yenilikçi bir yaklaşım önermektedir. Önerilen model, daha önce geliştirilen tekniklere kıyasla sayısal hataları önemli ölçüde azaltır. Ayrıca sunulan modelin sayısal sonuçları analitik çözüme oldukça yakındır. Son olarak, diğer araştırmacıların işini kolaylaştırmak için konveksiyon-difüzyon denklemi için sayısal ve analitik çözümlerin tüm Matlab kodları Ek'e dahil edilmiştir.

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Cite This Article

ÜNAL, O., AKKAŞ, N. (2022). An Innovative Approach for Numerical Solution of the Unsteady Convection-Dominated Flow Problems. Karadeniz Fen Bilimleri Dergisi, Cilt: 12 - Sayı: 2, 1069–1080. https://ajindex.com/articles/860756

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