An efficient algorithm for computing smoothness indicators for WENO schemes
WENO schemes are a popular class of shock-capturing schemes which adopt an adaptive-stencil approach to interpolation. WENO schemes rely on smoothness indicators to assess the relative smoothness of the solution within the sub-stencils. Computing these smoothness indicators is the most expensive ope...
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| Format: | Journal Article |
| Language: | English |
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2022
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| Online Access: | https://hdl.handle.net/10356/163937 |
| _version_ | 1811689595546370048 |
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| author | Vevek, U. S. |
| author2 | School of Mechanical and Aerospace Engineering |
| author_facet | School of Mechanical and Aerospace Engineering Vevek, U. S. |
| author_sort | Vevek, U. S. |
| collection | NTU |
| description | WENO schemes are a popular class of shock-capturing schemes which adopt an adaptive-stencil approach to interpolation. WENO schemes rely on smoothness indicators to assess the relative smoothness of the solution within the sub-stencils. Computing these smoothness indicators is the most expensive operation in the WENO reconstruction procedure. In this paper, an efficient algorithm is proposed to compute these quantities without sacrificing the positivity property of the smoothness indicators. The proposed algorithm involves linear combinations of the undivided differences which can be computed efficiently in a recursive manner. This allows the computation of the smoothness indicators to be performed using significantly fewer floating-point operations compared to conventional implementations. Moreover, the proposed algorithm is simple to implement and involves fewer constants. |
| first_indexed | 2024-10-01T05:50:36Z |
| format | Journal Article |
| id | ntu-10356/163937 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:50:36Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1639372022-12-22T07:20:48Z An efficient algorithm for computing smoothness indicators for WENO schemes Vevek, U. S. School of Mechanical and Aerospace Engineering Engineering::Mechanical engineering Smoothness Indicators Implementation WENO schemes are a popular class of shock-capturing schemes which adopt an adaptive-stencil approach to interpolation. WENO schemes rely on smoothness indicators to assess the relative smoothness of the solution within the sub-stencils. Computing these smoothness indicators is the most expensive operation in the WENO reconstruction procedure. In this paper, an efficient algorithm is proposed to compute these quantities without sacrificing the positivity property of the smoothness indicators. The proposed algorithm involves linear combinations of the undivided differences which can be computed efficiently in a recursive manner. This allows the computation of the smoothness indicators to be performed using significantly fewer floating-point operations compared to conventional implementations. Moreover, the proposed algorithm is simple to implement and involves fewer constants. 2022-12-22T07:20:47Z 2022-12-22T07:20:47Z 2021 Journal Article Vevek, U. S. (2021). An efficient algorithm for computing smoothness indicators for WENO schemes. Journal of Computational Physics, 446, 110619-. https://dx.doi.org/10.1016/j.jcp.2021.110619 0021-9991 https://hdl.handle.net/10356/163937 10.1016/j.jcp.2021.110619 2-s2.0-85113844663 446 110619 en Journal of Computational Physics © 2021 Elsevier Inc. All rights reserved. |
| spellingShingle | Engineering::Mechanical engineering Smoothness Indicators Implementation Vevek, U. S. An efficient algorithm for computing smoothness indicators for WENO schemes |
| title | An efficient algorithm for computing smoothness indicators for WENO schemes |
| title_full | An efficient algorithm for computing smoothness indicators for WENO schemes |
| title_fullStr | An efficient algorithm for computing smoothness indicators for WENO schemes |
| title_full_unstemmed | An efficient algorithm for computing smoothness indicators for WENO schemes |
| title_short | An efficient algorithm for computing smoothness indicators for WENO schemes |
| title_sort | efficient algorithm for computing smoothness indicators for weno schemes |
| topic | Engineering::Mechanical engineering Smoothness Indicators Implementation |
| url | https://hdl.handle.net/10356/163937 |
| work_keys_str_mv | AT vevekus anefficientalgorithmforcomputingsmoothnessindicatorsforwenoschemes AT vevekus efficientalgorithmforcomputingsmoothnessindicatorsforwenoschemes |