Prediction of Dynamic Stability Using Mapped Chebyshev Pseudospectral Method
A mapped Chebyshev pseudospectral method is extended to solve three-dimensional unsteady flow problems. As the classical Chebyshev spectral approach can lead to numerical instabilities due to ill conditioning of the spectral matrix, the Chebyshev points are evenly redistributed over the domain by an...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | International Journal of Aerospace Engineering |
| Online Access: | http://dx.doi.org/10.1155/2018/2508153 |
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| _version_ | 1832553655489789952 |
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| author | Jae-Young Choi Dong Kyun Im Jangho Park Seongim Choi |
| author_facet | Jae-Young Choi Dong Kyun Im Jangho Park Seongim Choi |
| author_sort | Jae-Young Choi |
| collection | DOAJ |
| description | A mapped Chebyshev pseudospectral method is extended to solve three-dimensional unsteady flow problems. As the classical Chebyshev spectral approach can lead to numerical instabilities due to ill conditioning of the spectral matrix, the Chebyshev points are evenly redistributed over the domain by an inverse sine mapping function. The mapped Chebyshev pseudospectral method can be used as an alternative time-spectral approach that uses a Chebyshev collocation operator to approximate the time derivative terms in the unsteady flow governing equations, and the method can make general applications to both nonperiodic and periodic problems. In this study, the mapped Chebyshev pseudospectral method is employed to solve three-dimensional periodic problem to verify the spectral accuracy and computational efficiency with those of the Fourier pseudospectral method and the time-accurate method. The results show a good agreement with both of the Fourier pseudospectral method and the time-accurate method. The flow solutions also demonstrate a good agreement with the experimental data. Similar to the Fourier pseudospectral method, the mapped Chebyshev pseudospectral method approximates the unsteady flow solutions with a precise accuracy at a considerably effective computational cost compared to the conventional time-accurate method. |
| format | Article |
| id | doaj-art-03b36f40884c41dc8569002d37ae5e40 |
| institution | Kabale University |
| issn | 1687-5966 1687-5974 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Aerospace Engineering |
| spelling | doaj-art-03b36f40884c41dc8569002d37ae5e402025-02-03T05:53:32ZengWileyInternational Journal of Aerospace Engineering1687-59661687-59742018-01-01201810.1155/2018/25081532508153Prediction of Dynamic Stability Using Mapped Chebyshev Pseudospectral MethodJae-Young Choi0Dong Kyun Im1Jangho Park2Seongim Choi3Aerospace and Ocean Engineering Department, Virginia Tech, Blacksburg, VA 24061, USADepartment of Mechanical Design Engineering, Youngsan University, Yangsan, Republic of KoreaAerospace and Ocean Engineering Department, Virginia Tech, Blacksburg, VA 24061, USAAerospace and Ocean Engineering Department, Virginia Tech, Blacksburg, VA 24061, USAA mapped Chebyshev pseudospectral method is extended to solve three-dimensional unsteady flow problems. As the classical Chebyshev spectral approach can lead to numerical instabilities due to ill conditioning of the spectral matrix, the Chebyshev points are evenly redistributed over the domain by an inverse sine mapping function. The mapped Chebyshev pseudospectral method can be used as an alternative time-spectral approach that uses a Chebyshev collocation operator to approximate the time derivative terms in the unsteady flow governing equations, and the method can make general applications to both nonperiodic and periodic problems. In this study, the mapped Chebyshev pseudospectral method is employed to solve three-dimensional periodic problem to verify the spectral accuracy and computational efficiency with those of the Fourier pseudospectral method and the time-accurate method. The results show a good agreement with both of the Fourier pseudospectral method and the time-accurate method. The flow solutions also demonstrate a good agreement with the experimental data. Similar to the Fourier pseudospectral method, the mapped Chebyshev pseudospectral method approximates the unsteady flow solutions with a precise accuracy at a considerably effective computational cost compared to the conventional time-accurate method.http://dx.doi.org/10.1155/2018/2508153 |
| spellingShingle | Jae-Young Choi Dong Kyun Im Jangho Park Seongim Choi Prediction of Dynamic Stability Using Mapped Chebyshev Pseudospectral Method International Journal of Aerospace Engineering |
| title | Prediction of Dynamic Stability Using Mapped Chebyshev Pseudospectral Method |
| title_full | Prediction of Dynamic Stability Using Mapped Chebyshev Pseudospectral Method |
| title_fullStr | Prediction of Dynamic Stability Using Mapped Chebyshev Pseudospectral Method |
| title_full_unstemmed | Prediction of Dynamic Stability Using Mapped Chebyshev Pseudospectral Method |
| title_short | Prediction of Dynamic Stability Using Mapped Chebyshev Pseudospectral Method |
| title_sort | prediction of dynamic stability using mapped chebyshev pseudospectral method |
| url | http://dx.doi.org/10.1155/2018/2508153 |
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