Optimized Weighted Essentially Nonoscillatory Third-Order Schemes for Hyperbolic Conservation Laws
We describe briefly how a third-order Weighted Essentially Nonoscillatory (WENO) scheme is derived by coupling a WENO spatial discretization scheme with a temporal integration scheme. The scheme is termed WENO3. We perform a spectral analysis of its dispersive and dissipative properties when used to...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/428681 |
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| author | A. R. Appadu A. A. I. Peer |
| author_facet | A. R. Appadu A. A. I. Peer |
| author_sort | A. R. Appadu |
| collection | DOAJ |
| description | We describe briefly how a third-order Weighted Essentially Nonoscillatory (WENO)
scheme is derived by coupling a WENO spatial discretization scheme with a temporal integration
scheme. The scheme is termed WENO3. We perform a spectral analysis of its dispersive and dissipative
properties when used to approximate the 1D linear advection equation and use a technique of
optimisation to find the optimal cfl number of the scheme. We carry out some numerical experiments
dealing with wave propagation based on the 1D linear advection and 1D Burger’s equation at some
different cfl numbers and show that the optimal cfl does indeed cause less dispersion, less dissipation,
and lower L1 errors. Lastly, we test numerically the order of convergence of the WENO3 scheme. |
| format | Article |
| id | doaj-art-9bfcca1268114a1594fbef98957fba4d |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-9bfcca1268114a1594fbef98957fba4d2025-02-03T06:01:50ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/428681428681Optimized Weighted Essentially Nonoscillatory Third-Order Schemes for Hyperbolic Conservation LawsA. R. Appadu0A. A. I. Peer1Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South AfricaDepartment of Applied Mathematical Sciences, University of Technology, Mauritius, La Tour Koenig, Pointe-aux-Sables, MauritiusWe describe briefly how a third-order Weighted Essentially Nonoscillatory (WENO) scheme is derived by coupling a WENO spatial discretization scheme with a temporal integration scheme. The scheme is termed WENO3. We perform a spectral analysis of its dispersive and dissipative properties when used to approximate the 1D linear advection equation and use a technique of optimisation to find the optimal cfl number of the scheme. We carry out some numerical experiments dealing with wave propagation based on the 1D linear advection and 1D Burger’s equation at some different cfl numbers and show that the optimal cfl does indeed cause less dispersion, less dissipation, and lower L1 errors. Lastly, we test numerically the order of convergence of the WENO3 scheme.http://dx.doi.org/10.1155/2013/428681 |
| spellingShingle | A. R. Appadu A. A. I. Peer Optimized Weighted Essentially Nonoscillatory Third-Order Schemes for Hyperbolic Conservation Laws Journal of Applied Mathematics |
| title | Optimized Weighted Essentially Nonoscillatory Third-Order Schemes for Hyperbolic Conservation Laws |
| title_full | Optimized Weighted Essentially Nonoscillatory Third-Order Schemes for Hyperbolic Conservation Laws |
| title_fullStr | Optimized Weighted Essentially Nonoscillatory Third-Order Schemes for Hyperbolic Conservation Laws |
| title_full_unstemmed | Optimized Weighted Essentially Nonoscillatory Third-Order Schemes for Hyperbolic Conservation Laws |
| title_short | Optimized Weighted Essentially Nonoscillatory Third-Order Schemes for Hyperbolic Conservation Laws |
| title_sort | optimized weighted essentially nonoscillatory third order schemes for hyperbolic conservation laws |
| url | http://dx.doi.org/10.1155/2013/428681 |
| work_keys_str_mv | AT arappadu optimizedweightedessentiallynonoscillatorythirdorderschemesforhyperbolicconservationlaws AT aaipeer optimizedweightedessentiallynonoscillatorythirdorderschemesforhyperbolicconservationlaws |