A Very High-Order Spatial Lagrange Interpolating Polynomial Scheme
This paper presents the extension of the Lagrange Interpolating Polynomial (LIP) scheme for solving differential equations by using the finite volume method called the Very high-order Spatial Lagrange Interpolating Polynomial (VS-LIP) scheme. The advantage of the VS-LIP scheme is its convenience for...
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| Format: | Article |
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Shahid Chamran University of Ahvaz
2025-07-01
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| Series: | Journal of Applied and Computational Mechanics |
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| Online Access: | https://jacm.scu.ac.ir/article_19436_5872ec28a9085c7384692eba6f62e4b6.pdf |
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| _version_ | 1849323045142921216 |
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| author | Uthai Prasopchingchana |
| author_facet | Uthai Prasopchingchana |
| author_sort | Uthai Prasopchingchana |
| collection | DOAJ |
| description | This paper presents the extension of the Lagrange Interpolating Polynomial (LIP) scheme for solving differential equations by using the finite volume method called the Very high-order Spatial Lagrange Interpolating Polynomial (VS-LIP) scheme. The advantage of the VS-LIP scheme is its convenience for extending the order of accuracy. The correctness of the VS-LIP scheme solutions is assessed by comparing the solutions with analytical, benchmark, published, and experimental solutions of five verification problems involving one- and two-dimensional heat transfer and fluid flow. The assessment is carried out to the sixth and twelfth orders of spatial accuracy. The assessment results indicated that the VS-LIP scheme delivers the correct solutions. |
| format | Article |
| id | doaj-art-12555616baf84b58a9979ebfb2cdc51d |
| institution | Kabale University |
| issn | 2383-4536 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Shahid Chamran University of Ahvaz |
| record_format | Article |
| series | Journal of Applied and Computational Mechanics |
| spelling | doaj-art-12555616baf84b58a9979ebfb2cdc51d2025-08-20T03:49:12ZengShahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45362025-07-0111384486010.22055/jacm.2024.47901.482419436A Very High-Order Spatial Lagrange Interpolating Polynomial SchemeUthai Prasopchingchana0Department of Mechanical Engineering, Burapha University, Chonburi, 20131, ThailandThis paper presents the extension of the Lagrange Interpolating Polynomial (LIP) scheme for solving differential equations by using the finite volume method called the Very high-order Spatial Lagrange Interpolating Polynomial (VS-LIP) scheme. The advantage of the VS-LIP scheme is its convenience for extending the order of accuracy. The correctness of the VS-LIP scheme solutions is assessed by comparing the solutions with analytical, benchmark, published, and experimental solutions of five verification problems involving one- and two-dimensional heat transfer and fluid flow. The assessment is carried out to the sixth and twelfth orders of spatial accuracy. The assessment results indicated that the VS-LIP scheme delivers the correct solutions.https://jacm.scu.ac.ir/article_19436_5872ec28a9085c7384692eba6f62e4b6.pdfvery high-order spatial lagrange interpolating polynomial schemefinite volume methodheat conductionnatural convectionlid-driven cavity flow |
| spellingShingle | Uthai Prasopchingchana A Very High-Order Spatial Lagrange Interpolating Polynomial Scheme Journal of Applied and Computational Mechanics very high-order spatial lagrange interpolating polynomial scheme finite volume method heat conduction natural convection lid-driven cavity flow |
| title | A Very High-Order Spatial Lagrange Interpolating Polynomial Scheme |
| title_full | A Very High-Order Spatial Lagrange Interpolating Polynomial Scheme |
| title_fullStr | A Very High-Order Spatial Lagrange Interpolating Polynomial Scheme |
| title_full_unstemmed | A Very High-Order Spatial Lagrange Interpolating Polynomial Scheme |
| title_short | A Very High-Order Spatial Lagrange Interpolating Polynomial Scheme |
| title_sort | very high order spatial lagrange interpolating polynomial scheme |
| topic | very high-order spatial lagrange interpolating polynomial scheme finite volume method heat conduction natural convection lid-driven cavity flow |
| url | https://jacm.scu.ac.ir/article_19436_5872ec28a9085c7384692eba6f62e4b6.pdf |
| work_keys_str_mv | AT uthaiprasopchingchana averyhighorderspatiallagrangeinterpolatingpolynomialscheme AT uthaiprasopchingchana veryhighorderspatiallagrangeinterpolatingpolynomialscheme |