A new formulation of the Green function in water of finite depth at low frequencies
We consider the frequency-domain free-surface Green function (GF) of wave radiation and diffraction in water of finite depth which is important for the hydrodynamic analysis of floating bodies, in general, and some renewable devices in shallow water, in particular. Further to the sound decomposition...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Xie, Chunmei [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022transfer abstract |
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| Übergeordnetes Werk: |
Enthalten in: P-602 - The attitudes of students of high schools in Gjilan related to drug abuse - 2012, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:128 ; year:2022 ; pages:0 |
| Links: |
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| DOI / URN: |
10.1016/j.apor.2022.103357 |
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| 520 | |a We consider the frequency-domain free-surface Green function (GF) of wave radiation and diffraction in water of finite depth which is important for the hydrodynamic analysis of floating bodies, in general, and some renewable devices in shallow water, in particular. Further to the sound decomposition formulation presented in Chen (1993), in which two depth-effect functions are defined, a new analysis has been performed to obtain a new formulation. It is composed of the analytical part including all singular behaviors and oscillations, and the remaining part is well suited for numerical computations with an accuracy of order 1 0 − 8 . Furthermore, the formulation is developed that the remaining part is fully smoothly varying and then approximated by Chebyshev polynomials. Not only the Green function itself but also its first-order and second-order derivatives are numerically evaluated and approximated independently by polynomials. The analytical formulations plus polynomials are then used to enhance efficiency and accuracy. Unlike previous studies, the analytical part of the Green function contains explicitly the logarithmic singularity when the depth-scaled wavenumber tends to zero. Classically included in the ’smooth’ part, this singular term is then extracted and the remaining part is fully smooth and much better approximated with consistent accuracy of 1 0 − 6 and less partitions. Furthermore, the added-mass and damping coefficients around a hemisphere are given. | ||
| 520 | |a We consider the frequency-domain free-surface Green function (GF) of wave radiation and diffraction in water of finite depth which is important for the hydrodynamic analysis of floating bodies, in general, and some renewable devices in shallow water, in particular. Further to the sound decomposition formulation presented in Chen (1993), in which two depth-effect functions are defined, a new analysis has been performed to obtain a new formulation. It is composed of the analytical part including all singular behaviors and oscillations, and the remaining part is well suited for numerical computations with an accuracy of order 1 0 − 8 . Furthermore, the formulation is developed that the remaining part is fully smoothly varying and then approximated by Chebyshev polynomials. Not only the Green function itself but also its first-order and second-order derivatives are numerically evaluated and approximated independently by polynomials. The analytical formulations plus polynomials are then used to enhance efficiency and accuracy. Unlike previous studies, the analytical part of the Green function contains explicitly the logarithmic singularity when the depth-scaled wavenumber tends to zero. Classically included in the ’smooth’ part, this singular term is then extracted and the remaining part is fully smooth and much better approximated with consistent accuracy of 1 0 − 6 and less partitions. Furthermore, the added-mass and damping coefficients around a hemisphere are given. | ||
| 650 | 7 | |a Logarithmic singularity |2 Elsevier | |
| 650 | 7 | |a Finite waterdepth |2 Elsevier | |
| 650 | 7 | |a Green function |2 Elsevier | |
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| 700 | 1 | |a Housseine, Charaf Ouled |4 oth | |
| 700 | 1 | |a Chen, Xiaobo |4 oth | |
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10.1016/j.apor.2022.103357 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001925.pica (DE-627)ELV05915036X (ELSEVIER)S0141-1187(22)00288-7 DE-627 ger DE-627 rakwb eng 610 VZ 530 VZ 33.00 bkl Xie, Chunmei verfasserin aut A new formulation of the Green function in water of finite depth at low frequencies 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We consider the frequency-domain free-surface Green function (GF) of wave radiation and diffraction in water of finite depth which is important for the hydrodynamic analysis of floating bodies, in general, and some renewable devices in shallow water, in particular. Further to the sound decomposition formulation presented in Chen (1993), in which two depth-effect functions are defined, a new analysis has been performed to obtain a new formulation. It is composed of the analytical part including all singular behaviors and oscillations, and the remaining part is well suited for numerical computations with an accuracy of order 1 0 − 8 . Furthermore, the formulation is developed that the remaining part is fully smoothly varying and then approximated by Chebyshev polynomials. Not only the Green function itself but also its first-order and second-order derivatives are numerically evaluated and approximated independently by polynomials. The analytical formulations plus polynomials are then used to enhance efficiency and accuracy. Unlike previous studies, the analytical part of the Green function contains explicitly the logarithmic singularity when the depth-scaled wavenumber tends to zero. Classically included in the ’smooth’ part, this singular term is then extracted and the remaining part is fully smooth and much better approximated with consistent accuracy of 1 0 − 6 and less partitions. Furthermore, the added-mass and damping coefficients around a hemisphere are given. We consider the frequency-domain free-surface Green function (GF) of wave radiation and diffraction in water of finite depth which is important for the hydrodynamic analysis of floating bodies, in general, and some renewable devices in shallow water, in particular. Further to the sound decomposition formulation presented in Chen (1993), in which two depth-effect functions are defined, a new analysis has been performed to obtain a new formulation. It is composed of the analytical part including all singular behaviors and oscillations, and the remaining part is well suited for numerical computations with an accuracy of order 1 0 − 8 . Furthermore, the formulation is developed that the remaining part is fully smoothly varying and then approximated by Chebyshev polynomials. Not only the Green function itself but also its first-order and second-order derivatives are numerically evaluated and approximated independently by polynomials. The analytical formulations plus polynomials are then used to enhance efficiency and accuracy. Unlike previous studies, the analytical part of the Green function contains explicitly the logarithmic singularity when the depth-scaled wavenumber tends to zero. Classically included in the ’smooth’ part, this singular term is then extracted and the remaining part is fully smooth and much better approximated with consistent accuracy of 1 0 − 6 and less partitions. Furthermore, the added-mass and damping coefficients around a hemisphere are given. Logarithmic singularity Elsevier Finite waterdepth Elsevier Green function Elsevier Chebyshev polynomials Elsevier Housseine, Charaf Ouled oth Chen, Xiaobo oth Enthalten in Elsevier Science P-602 - The attitudes of students of high schools in Gjilan related to drug abuse 2012 Amsterdam [u.a.] (DE-627)ELV011183217 volume:128 year:2022 pages:0 https://doi.org/10.1016/j.apor.2022.103357 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 33.00 Physik: Allgemeines VZ AR 128 2022 0 |
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10.1016/j.apor.2022.103357 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001925.pica (DE-627)ELV05915036X (ELSEVIER)S0141-1187(22)00288-7 DE-627 ger DE-627 rakwb eng 610 VZ 530 VZ 33.00 bkl Xie, Chunmei verfasserin aut A new formulation of the Green function in water of finite depth at low frequencies 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We consider the frequency-domain free-surface Green function (GF) of wave radiation and diffraction in water of finite depth which is important for the hydrodynamic analysis of floating bodies, in general, and some renewable devices in shallow water, in particular. Further to the sound decomposition formulation presented in Chen (1993), in which two depth-effect functions are defined, a new analysis has been performed to obtain a new formulation. It is composed of the analytical part including all singular behaviors and oscillations, and the remaining part is well suited for numerical computations with an accuracy of order 1 0 − 8 . Furthermore, the formulation is developed that the remaining part is fully smoothly varying and then approximated by Chebyshev polynomials. Not only the Green function itself but also its first-order and second-order derivatives are numerically evaluated and approximated independently by polynomials. The analytical formulations plus polynomials are then used to enhance efficiency and accuracy. Unlike previous studies, the analytical part of the Green function contains explicitly the logarithmic singularity when the depth-scaled wavenumber tends to zero. Classically included in the ’smooth’ part, this singular term is then extracted and the remaining part is fully smooth and much better approximated with consistent accuracy of 1 0 − 6 and less partitions. Furthermore, the added-mass and damping coefficients around a hemisphere are given. We consider the frequency-domain free-surface Green function (GF) of wave radiation and diffraction in water of finite depth which is important for the hydrodynamic analysis of floating bodies, in general, and some renewable devices in shallow water, in particular. Further to the sound decomposition formulation presented in Chen (1993), in which two depth-effect functions are defined, a new analysis has been performed to obtain a new formulation. It is composed of the analytical part including all singular behaviors and oscillations, and the remaining part is well suited for numerical computations with an accuracy of order 1 0 − 8 . Furthermore, the formulation is developed that the remaining part is fully smoothly varying and then approximated by Chebyshev polynomials. Not only the Green function itself but also its first-order and second-order derivatives are numerically evaluated and approximated independently by polynomials. The analytical formulations plus polynomials are then used to enhance efficiency and accuracy. Unlike previous studies, the analytical part of the Green function contains explicitly the logarithmic singularity when the depth-scaled wavenumber tends to zero. Classically included in the ’smooth’ part, this singular term is then extracted and the remaining part is fully smooth and much better approximated with consistent accuracy of 1 0 − 6 and less partitions. Furthermore, the added-mass and damping coefficients around a hemisphere are given. Logarithmic singularity Elsevier Finite waterdepth Elsevier Green function Elsevier Chebyshev polynomials Elsevier Housseine, Charaf Ouled oth Chen, Xiaobo oth Enthalten in Elsevier Science P-602 - The attitudes of students of high schools in Gjilan related to drug abuse 2012 Amsterdam [u.a.] (DE-627)ELV011183217 volume:128 year:2022 pages:0 https://doi.org/10.1016/j.apor.2022.103357 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 33.00 Physik: Allgemeines VZ AR 128 2022 0 |
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10.1016/j.apor.2022.103357 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001925.pica (DE-627)ELV05915036X (ELSEVIER)S0141-1187(22)00288-7 DE-627 ger DE-627 rakwb eng 610 VZ 530 VZ 33.00 bkl Xie, Chunmei verfasserin aut A new formulation of the Green function in water of finite depth at low frequencies 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We consider the frequency-domain free-surface Green function (GF) of wave radiation and diffraction in water of finite depth which is important for the hydrodynamic analysis of floating bodies, in general, and some renewable devices in shallow water, in particular. Further to the sound decomposition formulation presented in Chen (1993), in which two depth-effect functions are defined, a new analysis has been performed to obtain a new formulation. It is composed of the analytical part including all singular behaviors and oscillations, and the remaining part is well suited for numerical computations with an accuracy of order 1 0 − 8 . Furthermore, the formulation is developed that the remaining part is fully smoothly varying and then approximated by Chebyshev polynomials. Not only the Green function itself but also its first-order and second-order derivatives are numerically evaluated and approximated independently by polynomials. The analytical formulations plus polynomials are then used to enhance efficiency and accuracy. Unlike previous studies, the analytical part of the Green function contains explicitly the logarithmic singularity when the depth-scaled wavenumber tends to zero. Classically included in the ’smooth’ part, this singular term is then extracted and the remaining part is fully smooth and much better approximated with consistent accuracy of 1 0 − 6 and less partitions. Furthermore, the added-mass and damping coefficients around a hemisphere are given. We consider the frequency-domain free-surface Green function (GF) of wave radiation and diffraction in water of finite depth which is important for the hydrodynamic analysis of floating bodies, in general, and some renewable devices in shallow water, in particular. Further to the sound decomposition formulation presented in Chen (1993), in which two depth-effect functions are defined, a new analysis has been performed to obtain a new formulation. It is composed of the analytical part including all singular behaviors and oscillations, and the remaining part is well suited for numerical computations with an accuracy of order 1 0 − 8 . Furthermore, the formulation is developed that the remaining part is fully smoothly varying and then approximated by Chebyshev polynomials. Not only the Green function itself but also its first-order and second-order derivatives are numerically evaluated and approximated independently by polynomials. The analytical formulations plus polynomials are then used to enhance efficiency and accuracy. Unlike previous studies, the analytical part of the Green function contains explicitly the logarithmic singularity when the depth-scaled wavenumber tends to zero. Classically included in the ’smooth’ part, this singular term is then extracted and the remaining part is fully smooth and much better approximated with consistent accuracy of 1 0 − 6 and less partitions. Furthermore, the added-mass and damping coefficients around a hemisphere are given. Logarithmic singularity Elsevier Finite waterdepth Elsevier Green function Elsevier Chebyshev polynomials Elsevier Housseine, Charaf Ouled oth Chen, Xiaobo oth Enthalten in Elsevier Science P-602 - The attitudes of students of high schools in Gjilan related to drug abuse 2012 Amsterdam [u.a.] (DE-627)ELV011183217 volume:128 year:2022 pages:0 https://doi.org/10.1016/j.apor.2022.103357 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 33.00 Physik: Allgemeines VZ AR 128 2022 0 |
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10.1016/j.apor.2022.103357 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001925.pica (DE-627)ELV05915036X (ELSEVIER)S0141-1187(22)00288-7 DE-627 ger DE-627 rakwb eng 610 VZ 530 VZ 33.00 bkl Xie, Chunmei verfasserin aut A new formulation of the Green function in water of finite depth at low frequencies 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We consider the frequency-domain free-surface Green function (GF) of wave radiation and diffraction in water of finite depth which is important for the hydrodynamic analysis of floating bodies, in general, and some renewable devices in shallow water, in particular. Further to the sound decomposition formulation presented in Chen (1993), in which two depth-effect functions are defined, a new analysis has been performed to obtain a new formulation. It is composed of the analytical part including all singular behaviors and oscillations, and the remaining part is well suited for numerical computations with an accuracy of order 1 0 − 8 . Furthermore, the formulation is developed that the remaining part is fully smoothly varying and then approximated by Chebyshev polynomials. Not only the Green function itself but also its first-order and second-order derivatives are numerically evaluated and approximated independently by polynomials. The analytical formulations plus polynomials are then used to enhance efficiency and accuracy. Unlike previous studies, the analytical part of the Green function contains explicitly the logarithmic singularity when the depth-scaled wavenumber tends to zero. Classically included in the ’smooth’ part, this singular term is then extracted and the remaining part is fully smooth and much better approximated with consistent accuracy of 1 0 − 6 and less partitions. Furthermore, the added-mass and damping coefficients around a hemisphere are given. We consider the frequency-domain free-surface Green function (GF) of wave radiation and diffraction in water of finite depth which is important for the hydrodynamic analysis of floating bodies, in general, and some renewable devices in shallow water, in particular. Further to the sound decomposition formulation presented in Chen (1993), in which two depth-effect functions are defined, a new analysis has been performed to obtain a new formulation. It is composed of the analytical part including all singular behaviors and oscillations, and the remaining part is well suited for numerical computations with an accuracy of order 1 0 − 8 . Furthermore, the formulation is developed that the remaining part is fully smoothly varying and then approximated by Chebyshev polynomials. Not only the Green function itself but also its first-order and second-order derivatives are numerically evaluated and approximated independently by polynomials. The analytical formulations plus polynomials are then used to enhance efficiency and accuracy. Unlike previous studies, the analytical part of the Green function contains explicitly the logarithmic singularity when the depth-scaled wavenumber tends to zero. Classically included in the ’smooth’ part, this singular term is then extracted and the remaining part is fully smooth and much better approximated with consistent accuracy of 1 0 − 6 and less partitions. Furthermore, the added-mass and damping coefficients around a hemisphere are given. Logarithmic singularity Elsevier Finite waterdepth Elsevier Green function Elsevier Chebyshev polynomials Elsevier Housseine, Charaf Ouled oth Chen, Xiaobo oth Enthalten in Elsevier Science P-602 - The attitudes of students of high schools in Gjilan related to drug abuse 2012 Amsterdam [u.a.] (DE-627)ELV011183217 volume:128 year:2022 pages:0 https://doi.org/10.1016/j.apor.2022.103357 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 33.00 Physik: Allgemeines VZ AR 128 2022 0 |
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10.1016/j.apor.2022.103357 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001925.pica (DE-627)ELV05915036X (ELSEVIER)S0141-1187(22)00288-7 DE-627 ger DE-627 rakwb eng 610 VZ 530 VZ 33.00 bkl Xie, Chunmei verfasserin aut A new formulation of the Green function in water of finite depth at low frequencies 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier We consider the frequency-domain free-surface Green function (GF) of wave radiation and diffraction in water of finite depth which is important for the hydrodynamic analysis of floating bodies, in general, and some renewable devices in shallow water, in particular. Further to the sound decomposition formulation presented in Chen (1993), in which two depth-effect functions are defined, a new analysis has been performed to obtain a new formulation. It is composed of the analytical part including all singular behaviors and oscillations, and the remaining part is well suited for numerical computations with an accuracy of order 1 0 − 8 . Furthermore, the formulation is developed that the remaining part is fully smoothly varying and then approximated by Chebyshev polynomials. Not only the Green function itself but also its first-order and second-order derivatives are numerically evaluated and approximated independently by polynomials. The analytical formulations plus polynomials are then used to enhance efficiency and accuracy. Unlike previous studies, the analytical part of the Green function contains explicitly the logarithmic singularity when the depth-scaled wavenumber tends to zero. Classically included in the ’smooth’ part, this singular term is then extracted and the remaining part is fully smooth and much better approximated with consistent accuracy of 1 0 − 6 and less partitions. Furthermore, the added-mass and damping coefficients around a hemisphere are given. We consider the frequency-domain free-surface Green function (GF) of wave radiation and diffraction in water of finite depth which is important for the hydrodynamic analysis of floating bodies, in general, and some renewable devices in shallow water, in particular. Further to the sound decomposition formulation presented in Chen (1993), in which two depth-effect functions are defined, a new analysis has been performed to obtain a new formulation. It is composed of the analytical part including all singular behaviors and oscillations, and the remaining part is well suited for numerical computations with an accuracy of order 1 0 − 8 . Furthermore, the formulation is developed that the remaining part is fully smoothly varying and then approximated by Chebyshev polynomials. Not only the Green function itself but also its first-order and second-order derivatives are numerically evaluated and approximated independently by polynomials. The analytical formulations plus polynomials are then used to enhance efficiency and accuracy. Unlike previous studies, the analytical part of the Green function contains explicitly the logarithmic singularity when the depth-scaled wavenumber tends to zero. Classically included in the ’smooth’ part, this singular term is then extracted and the remaining part is fully smooth and much better approximated with consistent accuracy of 1 0 − 6 and less partitions. Furthermore, the added-mass and damping coefficients around a hemisphere are given. Logarithmic singularity Elsevier Finite waterdepth Elsevier Green function Elsevier Chebyshev polynomials Elsevier Housseine, Charaf Ouled oth Chen, Xiaobo oth Enthalten in Elsevier Science P-602 - The attitudes of students of high schools in Gjilan related to drug abuse 2012 Amsterdam [u.a.] (DE-627)ELV011183217 volume:128 year:2022 pages:0 https://doi.org/10.1016/j.apor.2022.103357 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U 33.00 Physik: Allgemeines VZ AR 128 2022 0 |
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a new formulation of the green function in water of finite depth at low frequencies |
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A new formulation of the Green function in water of finite depth at low frequencies |
| abstract |
We consider the frequency-domain free-surface Green function (GF) of wave radiation and diffraction in water of finite depth which is important for the hydrodynamic analysis of floating bodies, in general, and some renewable devices in shallow water, in particular. Further to the sound decomposition formulation presented in Chen (1993), in which two depth-effect functions are defined, a new analysis has been performed to obtain a new formulation. It is composed of the analytical part including all singular behaviors and oscillations, and the remaining part is well suited for numerical computations with an accuracy of order 1 0 − 8 . Furthermore, the formulation is developed that the remaining part is fully smoothly varying and then approximated by Chebyshev polynomials. Not only the Green function itself but also its first-order and second-order derivatives are numerically evaluated and approximated independently by polynomials. The analytical formulations plus polynomials are then used to enhance efficiency and accuracy. Unlike previous studies, the analytical part of the Green function contains explicitly the logarithmic singularity when the depth-scaled wavenumber tends to zero. Classically included in the ’smooth’ part, this singular term is then extracted and the remaining part is fully smooth and much better approximated with consistent accuracy of 1 0 − 6 and less partitions. Furthermore, the added-mass and damping coefficients around a hemisphere are given. |
| abstractGer |
We consider the frequency-domain free-surface Green function (GF) of wave radiation and diffraction in water of finite depth which is important for the hydrodynamic analysis of floating bodies, in general, and some renewable devices in shallow water, in particular. Further to the sound decomposition formulation presented in Chen (1993), in which two depth-effect functions are defined, a new analysis has been performed to obtain a new formulation. It is composed of the analytical part including all singular behaviors and oscillations, and the remaining part is well suited for numerical computations with an accuracy of order 1 0 − 8 . Furthermore, the formulation is developed that the remaining part is fully smoothly varying and then approximated by Chebyshev polynomials. Not only the Green function itself but also its first-order and second-order derivatives are numerically evaluated and approximated independently by polynomials. The analytical formulations plus polynomials are then used to enhance efficiency and accuracy. Unlike previous studies, the analytical part of the Green function contains explicitly the logarithmic singularity when the depth-scaled wavenumber tends to zero. Classically included in the ’smooth’ part, this singular term is then extracted and the remaining part is fully smooth and much better approximated with consistent accuracy of 1 0 − 6 and less partitions. Furthermore, the added-mass and damping coefficients around a hemisphere are given. |
| abstract_unstemmed |
We consider the frequency-domain free-surface Green function (GF) of wave radiation and diffraction in water of finite depth which is important for the hydrodynamic analysis of floating bodies, in general, and some renewable devices in shallow water, in particular. Further to the sound decomposition formulation presented in Chen (1993), in which two depth-effect functions are defined, a new analysis has been performed to obtain a new formulation. It is composed of the analytical part including all singular behaviors and oscillations, and the remaining part is well suited for numerical computations with an accuracy of order 1 0 − 8 . Furthermore, the formulation is developed that the remaining part is fully smoothly varying and then approximated by Chebyshev polynomials. Not only the Green function itself but also its first-order and second-order derivatives are numerically evaluated and approximated independently by polynomials. The analytical formulations plus polynomials are then used to enhance efficiency and accuracy. Unlike previous studies, the analytical part of the Green function contains explicitly the logarithmic singularity when the depth-scaled wavenumber tends to zero. Classically included in the ’smooth’ part, this singular term is then extracted and the remaining part is fully smooth and much better approximated with consistent accuracy of 1 0 − 6 and less partitions. Furthermore, the added-mass and damping coefficients around a hemisphere are given. |
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A new formulation of the Green function in water of finite depth at low frequencies |
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