A Numerical Study of an Operator Splitting Method for Rotating Flows with Large Ageostrophic Initial Data
Abstract: We propose an operator splitting method which is especially suitable for long-time integration of geophysical equations characterized by the presence of multiple-time scales and weak-operator splitting. The method is illustrated on the classical rotating shallow-water equations on a period...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Jones, D.A. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1999 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 1999 |
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| Übergeordnetes Werk: |
Enthalten in: Theoretical and computational fluid dynamics - Springer-Verlag, 1989, 13(1999), 2 vom: Juni, Seite 143-159 |
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| Übergeordnetes Werk: |
volume:13 ; year:1999 ; number:2 ; month:06 ; pages:143-159 |
| Links: |
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| DOI / URN: |
10.1007/s001620050012 |
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| Katalog-ID: |
OLC2071160754 |
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| 100 | 1 | |a Jones, D.A. |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a A Numerical Study of an Operator Splitting Method for Rotating Flows with Large Ageostrophic Initial Data |
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| 520 | |a Abstract: We propose an operator splitting method which is especially suitable for long-time integration of geophysical equations characterized by the presence of multiple-time scales and weak-operator splitting. The method is illustrated on the classical rotating shallow-water equations on a periodic domain with large ageostrophic (unprepared) initial data. The asymptotic splitting decomposes the solution into a first part which solves the quasigeostrophic equation; a second one which is the “slow” ageostrophic component of the flow; and a corrector. The particular decomposition we use ensures that the corrector is small for large rotation. By considering only the “slow” ageostrophic and quasigeostrophic components a numerical approximation to the shallow-water equations is derived that effectively removes the time-step restrictions caused by the presence of fast waves. The splitting is exact in the asymptotic limit of large rotation and includes the nonlinearity of the equations. Numerical examples are included. These examples demonstrate a significant reduction in the computational cost over direct numerical approximations of the shallow-water equations. We conclude with an outline of a general operator splitting method for more general primitive geophysical equations. | ||
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| 650 | 4 | |a Numerical Approximation | |
| 650 | 4 | |a General Operator | |
| 650 | 4 | |a Asymptotic Limit | |
| 700 | 1 | |a Mahalov, A. |4 aut | |
| 700 | 1 | |a Nicolaenko, B. |4 aut | |
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10.1007/s001620050012 doi (DE-627)OLC2071160754 (DE-He213)s001620050012-p DE-627 ger DE-627 rakwb eng 530 620 VZ 510 530 VZ Jones, D.A. verfasserin aut A Numerical Study of an Operator Splitting Method for Rotating Flows with Large Ageostrophic Initial Data 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1999 Abstract: We propose an operator splitting method which is especially suitable for long-time integration of geophysical equations characterized by the presence of multiple-time scales and weak-operator splitting. The method is illustrated on the classical rotating shallow-water equations on a periodic domain with large ageostrophic (unprepared) initial data. The asymptotic splitting decomposes the solution into a first part which solves the quasigeostrophic equation; a second one which is the “slow” ageostrophic component of the flow; and a corrector. The particular decomposition we use ensures that the corrector is small for large rotation. By considering only the “slow” ageostrophic and quasigeostrophic components a numerical approximation to the shallow-water equations is derived that effectively removes the time-step restrictions caused by the presence of fast waves. The splitting is exact in the asymptotic limit of large rotation and includes the nonlinearity of the equations. Numerical examples are included. These examples demonstrate a significant reduction in the computational cost over direct numerical approximations of the shallow-water equations. We conclude with an outline of a general operator splitting method for more general primitive geophysical equations. Initial Data Computational Cost Numerical Approximation General Operator Asymptotic Limit Mahalov, A. aut Nicolaenko, B. aut Enthalten in Theoretical and computational fluid dynamics Springer-Verlag, 1989 13(1999), 2 vom: Juni, Seite 143-159 (DE-627)130799521 (DE-600)1007949-X (DE-576)023042370 0935-4964 nnns volume:13 year:1999 number:2 month:06 pages:143-159 https://doi.org/10.1007/s001620050012 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2050 GBV_ILN_2354 GBV_ILN_4277 GBV_ILN_4302 GBV_ILN_4307 AR 13 1999 2 06 143-159 |
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10.1007/s001620050012 doi (DE-627)OLC2071160754 (DE-He213)s001620050012-p DE-627 ger DE-627 rakwb eng 530 620 VZ 510 530 VZ Jones, D.A. verfasserin aut A Numerical Study of an Operator Splitting Method for Rotating Flows with Large Ageostrophic Initial Data 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1999 Abstract: We propose an operator splitting method which is especially suitable for long-time integration of geophysical equations characterized by the presence of multiple-time scales and weak-operator splitting. The method is illustrated on the classical rotating shallow-water equations on a periodic domain with large ageostrophic (unprepared) initial data. The asymptotic splitting decomposes the solution into a first part which solves the quasigeostrophic equation; a second one which is the “slow” ageostrophic component of the flow; and a corrector. The particular decomposition we use ensures that the corrector is small for large rotation. By considering only the “slow” ageostrophic and quasigeostrophic components a numerical approximation to the shallow-water equations is derived that effectively removes the time-step restrictions caused by the presence of fast waves. The splitting is exact in the asymptotic limit of large rotation and includes the nonlinearity of the equations. Numerical examples are included. These examples demonstrate a significant reduction in the computational cost over direct numerical approximations of the shallow-water equations. We conclude with an outline of a general operator splitting method for more general primitive geophysical equations. Initial Data Computational Cost Numerical Approximation General Operator Asymptotic Limit Mahalov, A. aut Nicolaenko, B. aut Enthalten in Theoretical and computational fluid dynamics Springer-Verlag, 1989 13(1999), 2 vom: Juni, Seite 143-159 (DE-627)130799521 (DE-600)1007949-X (DE-576)023042370 0935-4964 nnns volume:13 year:1999 number:2 month:06 pages:143-159 https://doi.org/10.1007/s001620050012 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2050 GBV_ILN_2354 GBV_ILN_4277 GBV_ILN_4302 GBV_ILN_4307 AR 13 1999 2 06 143-159 |
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10.1007/s001620050012 doi (DE-627)OLC2071160754 (DE-He213)s001620050012-p DE-627 ger DE-627 rakwb eng 530 620 VZ 510 530 VZ Jones, D.A. verfasserin aut A Numerical Study of an Operator Splitting Method for Rotating Flows with Large Ageostrophic Initial Data 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1999 Abstract: We propose an operator splitting method which is especially suitable for long-time integration of geophysical equations characterized by the presence of multiple-time scales and weak-operator splitting. The method is illustrated on the classical rotating shallow-water equations on a periodic domain with large ageostrophic (unprepared) initial data. The asymptotic splitting decomposes the solution into a first part which solves the quasigeostrophic equation; a second one which is the “slow” ageostrophic component of the flow; and a corrector. The particular decomposition we use ensures that the corrector is small for large rotation. By considering only the “slow” ageostrophic and quasigeostrophic components a numerical approximation to the shallow-water equations is derived that effectively removes the time-step restrictions caused by the presence of fast waves. The splitting is exact in the asymptotic limit of large rotation and includes the nonlinearity of the equations. Numerical examples are included. These examples demonstrate a significant reduction in the computational cost over direct numerical approximations of the shallow-water equations. We conclude with an outline of a general operator splitting method for more general primitive geophysical equations. Initial Data Computational Cost Numerical Approximation General Operator Asymptotic Limit Mahalov, A. aut Nicolaenko, B. aut Enthalten in Theoretical and computational fluid dynamics Springer-Verlag, 1989 13(1999), 2 vom: Juni, Seite 143-159 (DE-627)130799521 (DE-600)1007949-X (DE-576)023042370 0935-4964 nnns volume:13 year:1999 number:2 month:06 pages:143-159 https://doi.org/10.1007/s001620050012 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2050 GBV_ILN_2354 GBV_ILN_4277 GBV_ILN_4302 GBV_ILN_4307 AR 13 1999 2 06 143-159 |
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10.1007/s001620050012 doi (DE-627)OLC2071160754 (DE-He213)s001620050012-p DE-627 ger DE-627 rakwb eng 530 620 VZ 510 530 VZ Jones, D.A. verfasserin aut A Numerical Study of an Operator Splitting Method for Rotating Flows with Large Ageostrophic Initial Data 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1999 Abstract: We propose an operator splitting method which is especially suitable for long-time integration of geophysical equations characterized by the presence of multiple-time scales and weak-operator splitting. The method is illustrated on the classical rotating shallow-water equations on a periodic domain with large ageostrophic (unprepared) initial data. The asymptotic splitting decomposes the solution into a first part which solves the quasigeostrophic equation; a second one which is the “slow” ageostrophic component of the flow; and a corrector. The particular decomposition we use ensures that the corrector is small for large rotation. By considering only the “slow” ageostrophic and quasigeostrophic components a numerical approximation to the shallow-water equations is derived that effectively removes the time-step restrictions caused by the presence of fast waves. The splitting is exact in the asymptotic limit of large rotation and includes the nonlinearity of the equations. Numerical examples are included. These examples demonstrate a significant reduction in the computational cost over direct numerical approximations of the shallow-water equations. We conclude with an outline of a general operator splitting method for more general primitive geophysical equations. Initial Data Computational Cost Numerical Approximation General Operator Asymptotic Limit Mahalov, A. aut Nicolaenko, B. aut Enthalten in Theoretical and computational fluid dynamics Springer-Verlag, 1989 13(1999), 2 vom: Juni, Seite 143-159 (DE-627)130799521 (DE-600)1007949-X (DE-576)023042370 0935-4964 nnns volume:13 year:1999 number:2 month:06 pages:143-159 https://doi.org/10.1007/s001620050012 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2050 GBV_ILN_2354 GBV_ILN_4277 GBV_ILN_4302 GBV_ILN_4307 AR 13 1999 2 06 143-159 |
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10.1007/s001620050012 doi (DE-627)OLC2071160754 (DE-He213)s001620050012-p DE-627 ger DE-627 rakwb eng 530 620 VZ 510 530 VZ Jones, D.A. verfasserin aut A Numerical Study of an Operator Splitting Method for Rotating Flows with Large Ageostrophic Initial Data 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1999 Abstract: We propose an operator splitting method which is especially suitable for long-time integration of geophysical equations characterized by the presence of multiple-time scales and weak-operator splitting. The method is illustrated on the classical rotating shallow-water equations on a periodic domain with large ageostrophic (unprepared) initial data. The asymptotic splitting decomposes the solution into a first part which solves the quasigeostrophic equation; a second one which is the “slow” ageostrophic component of the flow; and a corrector. The particular decomposition we use ensures that the corrector is small for large rotation. By considering only the “slow” ageostrophic and quasigeostrophic components a numerical approximation to the shallow-water equations is derived that effectively removes the time-step restrictions caused by the presence of fast waves. The splitting is exact in the asymptotic limit of large rotation and includes the nonlinearity of the equations. Numerical examples are included. These examples demonstrate a significant reduction in the computational cost over direct numerical approximations of the shallow-water equations. We conclude with an outline of a general operator splitting method for more general primitive geophysical equations. Initial Data Computational Cost Numerical Approximation General Operator Asymptotic Limit Mahalov, A. aut Nicolaenko, B. aut Enthalten in Theoretical and computational fluid dynamics Springer-Verlag, 1989 13(1999), 2 vom: Juni, Seite 143-159 (DE-627)130799521 (DE-600)1007949-X (DE-576)023042370 0935-4964 nnns volume:13 year:1999 number:2 month:06 pages:143-159 https://doi.org/10.1007/s001620050012 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_40 GBV_ILN_65 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2050 GBV_ILN_2354 GBV_ILN_4277 GBV_ILN_4302 GBV_ILN_4307 AR 13 1999 2 06 143-159 |
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Jones, D.A. |
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530 620 VZ 510 530 VZ A Numerical Study of an Operator Splitting Method for Rotating Flows with Large Ageostrophic Initial Data Initial Data Computational Cost Numerical Approximation General Operator Asymptotic Limit |
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A Numerical Study of an Operator Splitting Method for Rotating Flows with Large Ageostrophic Initial Data |
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A Numerical Study of an Operator Splitting Method for Rotating Flows with Large Ageostrophic Initial Data |
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Jones, D.A. |
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Theoretical and computational fluid dynamics |
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1999 |
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Jones, D.A. Mahalov, A. Nicolaenko, B. |
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Jones, D.A. |
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10.1007/s001620050012 |
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530 620 510 |
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a numerical study of an operator splitting method for rotating flows with large ageostrophic initial data |
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A Numerical Study of an Operator Splitting Method for Rotating Flows with Large Ageostrophic Initial Data |
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Abstract: We propose an operator splitting method which is especially suitable for long-time integration of geophysical equations characterized by the presence of multiple-time scales and weak-operator splitting. The method is illustrated on the classical rotating shallow-water equations on a periodic domain with large ageostrophic (unprepared) initial data. The asymptotic splitting decomposes the solution into a first part which solves the quasigeostrophic equation; a second one which is the “slow” ageostrophic component of the flow; and a corrector. The particular decomposition we use ensures that the corrector is small for large rotation. By considering only the “slow” ageostrophic and quasigeostrophic components a numerical approximation to the shallow-water equations is derived that effectively removes the time-step restrictions caused by the presence of fast waves. The splitting is exact in the asymptotic limit of large rotation and includes the nonlinearity of the equations. Numerical examples are included. These examples demonstrate a significant reduction in the computational cost over direct numerical approximations of the shallow-water equations. We conclude with an outline of a general operator splitting method for more general primitive geophysical equations. © Springer-Verlag Berlin Heidelberg 1999 |
| abstractGer |
Abstract: We propose an operator splitting method which is especially suitable for long-time integration of geophysical equations characterized by the presence of multiple-time scales and weak-operator splitting. The method is illustrated on the classical rotating shallow-water equations on a periodic domain with large ageostrophic (unprepared) initial data. The asymptotic splitting decomposes the solution into a first part which solves the quasigeostrophic equation; a second one which is the “slow” ageostrophic component of the flow; and a corrector. The particular decomposition we use ensures that the corrector is small for large rotation. By considering only the “slow” ageostrophic and quasigeostrophic components a numerical approximation to the shallow-water equations is derived that effectively removes the time-step restrictions caused by the presence of fast waves. The splitting is exact in the asymptotic limit of large rotation and includes the nonlinearity of the equations. Numerical examples are included. These examples demonstrate a significant reduction in the computational cost over direct numerical approximations of the shallow-water equations. We conclude with an outline of a general operator splitting method for more general primitive geophysical equations. © Springer-Verlag Berlin Heidelberg 1999 |
| abstract_unstemmed |
Abstract: We propose an operator splitting method which is especially suitable for long-time integration of geophysical equations characterized by the presence of multiple-time scales and weak-operator splitting. The method is illustrated on the classical rotating shallow-water equations on a periodic domain with large ageostrophic (unprepared) initial data. The asymptotic splitting decomposes the solution into a first part which solves the quasigeostrophic equation; a second one which is the “slow” ageostrophic component of the flow; and a corrector. The particular decomposition we use ensures that the corrector is small for large rotation. By considering only the “slow” ageostrophic and quasigeostrophic components a numerical approximation to the shallow-water equations is derived that effectively removes the time-step restrictions caused by the presence of fast waves. The splitting is exact in the asymptotic limit of large rotation and includes the nonlinearity of the equations. Numerical examples are included. These examples demonstrate a significant reduction in the computational cost over direct numerical approximations of the shallow-water equations. We conclude with an outline of a general operator splitting method for more general primitive geophysical equations. © Springer-Verlag Berlin Heidelberg 1999 |
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A Numerical Study of an Operator Splitting Method for Rotating Flows with Large Ageostrophic Initial Data |
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