An energy-stable generalized-α method for the Swift-Hohenberg equation
We propose a second-order accurate energy-stable time-integration method that controls the evolution of numerical instabilities introducing numerical dissipation in the highest-resolved frequencies. Our algorithm further extends the generalized-a method and provides control over dissipation via the...
| Main Authors: | , , , , , |
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| Format: | Journal Article |
| Published: |
Elsevier
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/63144 |
| _version_ | 1848761006671527936 |
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| author | Sarmiento, A. Espath, L. Vignal, P. Dalcin, L. Parsani, M. Calo, Victor |
| author_facet | Sarmiento, A. Espath, L. Vignal, P. Dalcin, L. Parsani, M. Calo, Victor |
| author_sort | Sarmiento, A. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We propose a second-order accurate energy-stable time-integration method that controls the evolution of numerical instabilities introducing numerical dissipation in the highest-resolved frequencies. Our algorithm further extends the generalized-a method and provides control over dissipation via the spectral radius. We derive the first and second laws of thermodynamics for the Swift-Hohenberg equation and provide a detailed proof of the unconditional energy stability of our algorithm. Finally, we present numerical results to verify the energy stability and its second-order accuracy in time. |
| first_indexed | 2025-11-14T10:24:49Z |
| format | Journal Article |
| id | curtin-20.500.11937-63144 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:24:49Z |
| publishDate | 2017 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-631442019-12-02T07:11:39Z An energy-stable generalized-α method for the Swift-Hohenberg equation Sarmiento, A. Espath, L. Vignal, P. Dalcin, L. Parsani, M. Calo, Victor We propose a second-order accurate energy-stable time-integration method that controls the evolution of numerical instabilities introducing numerical dissipation in the highest-resolved frequencies. Our algorithm further extends the generalized-a method and provides control over dissipation via the spectral radius. We derive the first and second laws of thermodynamics for the Swift-Hohenberg equation and provide a detailed proof of the unconditional energy stability of our algorithm. Finally, we present numerical results to verify the energy stability and its second-order accuracy in time. 2017 Journal Article http://hdl.handle.net/20.500.11937/63144 10.1016/j.cam.2017.11.004 Elsevier fulltext |
| spellingShingle | Sarmiento, A. Espath, L. Vignal, P. Dalcin, L. Parsani, M. Calo, Victor An energy-stable generalized-α method for the Swift-Hohenberg equation |
| title | An energy-stable generalized-α method for the Swift-Hohenberg equation |
| title_full | An energy-stable generalized-α method for the Swift-Hohenberg equation |
| title_fullStr | An energy-stable generalized-α method for the Swift-Hohenberg equation |
| title_full_unstemmed | An energy-stable generalized-α method for the Swift-Hohenberg equation |
| title_short | An energy-stable generalized-α method for the Swift-Hohenberg equation |
| title_sort | energy-stable generalized-α method for the swift-hohenberg equation |
| url | http://hdl.handle.net/20.500.11937/63144 |