RESEARCH ARTICLE
Application of high-resolution NVD differencing schemes to the FTn finite volume method for radiative heat transfer
Kamel Guedri,
Abdulmajeed Saeed Al-Ghamdi,
Mowffaq Oreijah,
Kamel Guedri
Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, B. Po 5555, Makkah, 21955 Saudi Arabia
Unité de Recherche : Matériaux, Energie et Energies Renouvelables (MEER), Faculty of Sciences of Gafsa, University of Gafsa, 2112 Gafsa, Tunisia
Search for more papers by this authorAbdulmajeed Saeed Al-Ghamdi
Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, B. Po 5555, Makkah, 21955 Saudi Arabia
Search for more papers by this authorMowffaq Oreijah
Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, B. Po 5555, Makkah, 21955 Saudi Arabia
Search for more papers by this authorKamel Guedri,
Abdulmajeed Saeed Al-Ghamdi,
Mowffaq Oreijah,
Kamel Guedri
Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, B. Po 5555, Makkah, 21955 Saudi Arabia
Unité de Recherche : Matériaux, Energie et Energies Renouvelables (MEER), Faculty of Sciences of Gafsa, University of Gafsa, 2112 Gafsa, Tunisia
Search for more papers by this authorAbdulmajeed Saeed Al-Ghamdi
Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, B. Po 5555, Makkah, 21955 Saudi Arabia
Search for more papers by this authorMowffaq Oreijah
Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al-Qura University, B. Po 5555, Makkah, 21955 Saudi Arabia
Search for more papers by this authorAbstract
In this work, the STEP scheme and several schemes based on the normalized variable diagram (NVD), such as MINMOD, GAMMA, CLAM, NOTABLE, MUSCL, CUBISTA, SMART, WACEB, and VANOS schemes, are evaluated for solving the radiative transfer equation. Two-dimensional and three-dimensional rectangular enclosures containing transparent, emitting–absorbing, emitting–absorbing–scattering, or nonhomogeneous participating media are investigated using the modified FTn finite volume method. Although the NVD schemes are much more accurate than the STEP scheme, but they have more time-consuming and require more iterations. Moreover, most of them often necessitate underrelaxation to ensure convergence. Results show that the MINMOD and GAMMA schemes are still much less accurate than other NVD schemes, but they converge the fastest of the NVD schemes, and do not require underrelaxation. Although the VANOS, WACEB, and SMART schemes give more accurate solutions, they are not competitive with other NVD schemes. However, the CLAM, NOTABLE, and CUBISTA schemes are relatively fast and accurate.
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