Application of high‐resolution NVD differencing schemes to the FTn finite volume method for radiative heat transfer |
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| Authors: | Kamel Guedri Abdulmajeed Saeed Al‐Ghamdi Mowffaq Oreijah |
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| Affiliation: | 1. Mechanical Engineering Department, College of Engineering and Islamic Architecture, Umm Al‐Qura University, Makkah, Saudi Arabia;2. Unité de Recherche 3. : Matériaux, Energie et Energies Renouvelables (MEER), Faculty of Sciences of Gafsa, University of Gafsa, Gafsa, Tunisia |
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| Abstract: | 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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| Keywords: | false scattering FTn finite volume method normalized variable diagram (NVD) schemes radiative heat transfer ray effects |
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