Existence and Stability of Multidimensional Transonic Flows through an Infinite Nozzle of Arbitrary Cross-Sections
Abstract We establish the existence and stability of multidimensional steady transonic flows with transonic shocks through an infinite nozzle of arbitrary cross-sections, including a slowly varying de Laval nozzle. The transonic flow is governed by the inviscid potential flow equation with supersoni...
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| Autor*in: |
Chen, Gui-Qiang [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2006 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 2006 |
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| Übergeordnetes Werk: |
Enthalten in: Archive for rational mechanics and analysis - Springer-Verlag, 1957, 184(2006), 2 vom: 18. Okt., Seite 185-242 |
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| Übergeordnetes Werk: |
volume:184 ; year:2006 ; number:2 ; day:18 ; month:10 ; pages:185-242 |
| Links: |
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| DOI / URN: |
10.1007/s00205-006-0025-5 |
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| Katalog-ID: |
OLC2056416077 |
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| 520 | |a Abstract We establish the existence and stability of multidimensional steady transonic flows with transonic shocks through an infinite nozzle of arbitrary cross-sections, including a slowly varying de Laval nozzle. The transonic flow is governed by the inviscid potential flow equation with supersonic upstream flow at the entrance, uniform subsonic downstream flow at the exit at infinity, and the slip boundary condition on the nozzle boundary. Our results indicate that, if the supersonic upstream flow at the entrance is sufficiently close to a uniform flow, there exists a solution that consists of a C1,α subsonic flow in the unbounded downstream region, converging to a uniform velocity state at infinity, and a C1,α multidimensional transonic shock separating the subsonic flow from the supersonic upstream flow; the uniform velocity state at the exit at infinity in the downstream direction is uniquely determined by the supersonic upstream flow; and the shock is orthogonal to the nozzle boundary at every point of their intersection. In order to construct such a transonic flow, we reformulate the multidimensional transonic nozzle problem into a free boundary problem for the subsonic phase, in which the equation is elliptic and the free boundary is a transonic shock. The free boundary conditions are determined by the Rankine–Hugoniot conditions along the shock. We further develop a nonlinear iteration approach and employ its advantages to deal with such a free boundary problem in the unbounded domain. We also prove that the transonic flow with a transonic shock is unique and stable with respect to the nozzle boundary and the smooth supersonic upstream flow at the entrance. | ||
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10.1007/s00205-006-0025-5 doi (DE-627)OLC2056416077 (DE-He213)s00205-006-0025-5-p DE-627 ger DE-627 rakwb eng 530 510 VZ Chen, Gui-Qiang verfasserin aut Existence and Stability of Multidimensional Transonic Flows through an Infinite Nozzle of Arbitrary Cross-Sections 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2006 Abstract We establish the existence and stability of multidimensional steady transonic flows with transonic shocks through an infinite nozzle of arbitrary cross-sections, including a slowly varying de Laval nozzle. The transonic flow is governed by the inviscid potential flow equation with supersonic upstream flow at the entrance, uniform subsonic downstream flow at the exit at infinity, and the slip boundary condition on the nozzle boundary. Our results indicate that, if the supersonic upstream flow at the entrance is sufficiently close to a uniform flow, there exists a solution that consists of a C1,α subsonic flow in the unbounded downstream region, converging to a uniform velocity state at infinity, and a C1,α multidimensional transonic shock separating the subsonic flow from the supersonic upstream flow; the uniform velocity state at the exit at infinity in the downstream direction is uniquely determined by the supersonic upstream flow; and the shock is orthogonal to the nozzle boundary at every point of their intersection. In order to construct such a transonic flow, we reformulate the multidimensional transonic nozzle problem into a free boundary problem for the subsonic phase, in which the equation is elliptic and the free boundary is a transonic shock. The free boundary conditions are determined by the Rankine–Hugoniot conditions along the shock. We further develop a nonlinear iteration approach and employ its advantages to deal with such a free boundary problem in the unbounded domain. We also prove that the transonic flow with a transonic shock is unique and stable with respect to the nozzle boundary and the smooth supersonic upstream flow at the entrance. Weak Solution Free Boundary Free Boundary Problem Nonlinear Wave Equation Transonic Flow Feldman, Mikhail aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 184(2006), 2 vom: 18. Okt., Seite 185-242 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:184 year:2006 number:2 day:18 month:10 pages:185-242 https://doi.org/10.1007/s00205-006-0025-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4323 GBV_ILN_4700 AR 184 2006 2 18 10 185-242 |
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10.1007/s00205-006-0025-5 doi (DE-627)OLC2056416077 (DE-He213)s00205-006-0025-5-p DE-627 ger DE-627 rakwb eng 530 510 VZ Chen, Gui-Qiang verfasserin aut Existence and Stability of Multidimensional Transonic Flows through an Infinite Nozzle of Arbitrary Cross-Sections 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2006 Abstract We establish the existence and stability of multidimensional steady transonic flows with transonic shocks through an infinite nozzle of arbitrary cross-sections, including a slowly varying de Laval nozzle. The transonic flow is governed by the inviscid potential flow equation with supersonic upstream flow at the entrance, uniform subsonic downstream flow at the exit at infinity, and the slip boundary condition on the nozzle boundary. Our results indicate that, if the supersonic upstream flow at the entrance is sufficiently close to a uniform flow, there exists a solution that consists of a C1,α subsonic flow in the unbounded downstream region, converging to a uniform velocity state at infinity, and a C1,α multidimensional transonic shock separating the subsonic flow from the supersonic upstream flow; the uniform velocity state at the exit at infinity in the downstream direction is uniquely determined by the supersonic upstream flow; and the shock is orthogonal to the nozzle boundary at every point of their intersection. In order to construct such a transonic flow, we reformulate the multidimensional transonic nozzle problem into a free boundary problem for the subsonic phase, in which the equation is elliptic and the free boundary is a transonic shock. The free boundary conditions are determined by the Rankine–Hugoniot conditions along the shock. We further develop a nonlinear iteration approach and employ its advantages to deal with such a free boundary problem in the unbounded domain. We also prove that the transonic flow with a transonic shock is unique and stable with respect to the nozzle boundary and the smooth supersonic upstream flow at the entrance. Weak Solution Free Boundary Free Boundary Problem Nonlinear Wave Equation Transonic Flow Feldman, Mikhail aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 184(2006), 2 vom: 18. Okt., Seite 185-242 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:184 year:2006 number:2 day:18 month:10 pages:185-242 https://doi.org/10.1007/s00205-006-0025-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4323 GBV_ILN_4700 AR 184 2006 2 18 10 185-242 |
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10.1007/s00205-006-0025-5 doi (DE-627)OLC2056416077 (DE-He213)s00205-006-0025-5-p DE-627 ger DE-627 rakwb eng 530 510 VZ Chen, Gui-Qiang verfasserin aut Existence and Stability of Multidimensional Transonic Flows through an Infinite Nozzle of Arbitrary Cross-Sections 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2006 Abstract We establish the existence and stability of multidimensional steady transonic flows with transonic shocks through an infinite nozzle of arbitrary cross-sections, including a slowly varying de Laval nozzle. The transonic flow is governed by the inviscid potential flow equation with supersonic upstream flow at the entrance, uniform subsonic downstream flow at the exit at infinity, and the slip boundary condition on the nozzle boundary. Our results indicate that, if the supersonic upstream flow at the entrance is sufficiently close to a uniform flow, there exists a solution that consists of a C1,α subsonic flow in the unbounded downstream region, converging to a uniform velocity state at infinity, and a C1,α multidimensional transonic shock separating the subsonic flow from the supersonic upstream flow; the uniform velocity state at the exit at infinity in the downstream direction is uniquely determined by the supersonic upstream flow; and the shock is orthogonal to the nozzle boundary at every point of their intersection. In order to construct such a transonic flow, we reformulate the multidimensional transonic nozzle problem into a free boundary problem for the subsonic phase, in which the equation is elliptic and the free boundary is a transonic shock. The free boundary conditions are determined by the Rankine–Hugoniot conditions along the shock. We further develop a nonlinear iteration approach and employ its advantages to deal with such a free boundary problem in the unbounded domain. We also prove that the transonic flow with a transonic shock is unique and stable with respect to the nozzle boundary and the smooth supersonic upstream flow at the entrance. Weak Solution Free Boundary Free Boundary Problem Nonlinear Wave Equation Transonic Flow Feldman, Mikhail aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 184(2006), 2 vom: 18. Okt., Seite 185-242 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:184 year:2006 number:2 day:18 month:10 pages:185-242 https://doi.org/10.1007/s00205-006-0025-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4323 GBV_ILN_4700 AR 184 2006 2 18 10 185-242 |
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10.1007/s00205-006-0025-5 doi (DE-627)OLC2056416077 (DE-He213)s00205-006-0025-5-p DE-627 ger DE-627 rakwb eng 530 510 VZ Chen, Gui-Qiang verfasserin aut Existence and Stability of Multidimensional Transonic Flows through an Infinite Nozzle of Arbitrary Cross-Sections 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2006 Abstract We establish the existence and stability of multidimensional steady transonic flows with transonic shocks through an infinite nozzle of arbitrary cross-sections, including a slowly varying de Laval nozzle. The transonic flow is governed by the inviscid potential flow equation with supersonic upstream flow at the entrance, uniform subsonic downstream flow at the exit at infinity, and the slip boundary condition on the nozzle boundary. Our results indicate that, if the supersonic upstream flow at the entrance is sufficiently close to a uniform flow, there exists a solution that consists of a C1,α subsonic flow in the unbounded downstream region, converging to a uniform velocity state at infinity, and a C1,α multidimensional transonic shock separating the subsonic flow from the supersonic upstream flow; the uniform velocity state at the exit at infinity in the downstream direction is uniquely determined by the supersonic upstream flow; and the shock is orthogonal to the nozzle boundary at every point of their intersection. In order to construct such a transonic flow, we reformulate the multidimensional transonic nozzle problem into a free boundary problem for the subsonic phase, in which the equation is elliptic and the free boundary is a transonic shock. The free boundary conditions are determined by the Rankine–Hugoniot conditions along the shock. We further develop a nonlinear iteration approach and employ its advantages to deal with such a free boundary problem in the unbounded domain. We also prove that the transonic flow with a transonic shock is unique and stable with respect to the nozzle boundary and the smooth supersonic upstream flow at the entrance. Weak Solution Free Boundary Free Boundary Problem Nonlinear Wave Equation Transonic Flow Feldman, Mikhail aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 184(2006), 2 vom: 18. Okt., Seite 185-242 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:184 year:2006 number:2 day:18 month:10 pages:185-242 https://doi.org/10.1007/s00205-006-0025-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4323 GBV_ILN_4700 AR 184 2006 2 18 10 185-242 |
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10.1007/s00205-006-0025-5 doi (DE-627)OLC2056416077 (DE-He213)s00205-006-0025-5-p DE-627 ger DE-627 rakwb eng 530 510 VZ Chen, Gui-Qiang verfasserin aut Existence and Stability of Multidimensional Transonic Flows through an Infinite Nozzle of Arbitrary Cross-Sections 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2006 Abstract We establish the existence and stability of multidimensional steady transonic flows with transonic shocks through an infinite nozzle of arbitrary cross-sections, including a slowly varying de Laval nozzle. The transonic flow is governed by the inviscid potential flow equation with supersonic upstream flow at the entrance, uniform subsonic downstream flow at the exit at infinity, and the slip boundary condition on the nozzle boundary. Our results indicate that, if the supersonic upstream flow at the entrance is sufficiently close to a uniform flow, there exists a solution that consists of a C1,α subsonic flow in the unbounded downstream region, converging to a uniform velocity state at infinity, and a C1,α multidimensional transonic shock separating the subsonic flow from the supersonic upstream flow; the uniform velocity state at the exit at infinity in the downstream direction is uniquely determined by the supersonic upstream flow; and the shock is orthogonal to the nozzle boundary at every point of their intersection. In order to construct such a transonic flow, we reformulate the multidimensional transonic nozzle problem into a free boundary problem for the subsonic phase, in which the equation is elliptic and the free boundary is a transonic shock. The free boundary conditions are determined by the Rankine–Hugoniot conditions along the shock. We further develop a nonlinear iteration approach and employ its advantages to deal with such a free boundary problem in the unbounded domain. We also prove that the transonic flow with a transonic shock is unique and stable with respect to the nozzle boundary and the smooth supersonic upstream flow at the entrance. Weak Solution Free Boundary Free Boundary Problem Nonlinear Wave Equation Transonic Flow Feldman, Mikhail aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 184(2006), 2 vom: 18. Okt., Seite 185-242 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:184 year:2006 number:2 day:18 month:10 pages:185-242 https://doi.org/10.1007/s00205-006-0025-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_62 GBV_ILN_65 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4027 GBV_ILN_4036 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4323 GBV_ILN_4700 AR 184 2006 2 18 10 185-242 |
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Enthalten in Archive for rational mechanics and analysis 184(2006), 2 vom: 18. Okt., Seite 185-242 volume:184 year:2006 number:2 day:18 month:10 pages:185-242 |
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existence and stability of multidimensional transonic flows through an infinite nozzle of arbitrary cross-sections |
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Existence and Stability of Multidimensional Transonic Flows through an Infinite Nozzle of Arbitrary Cross-Sections |
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Abstract We establish the existence and stability of multidimensional steady transonic flows with transonic shocks through an infinite nozzle of arbitrary cross-sections, including a slowly varying de Laval nozzle. The transonic flow is governed by the inviscid potential flow equation with supersonic upstream flow at the entrance, uniform subsonic downstream flow at the exit at infinity, and the slip boundary condition on the nozzle boundary. Our results indicate that, if the supersonic upstream flow at the entrance is sufficiently close to a uniform flow, there exists a solution that consists of a C1,α subsonic flow in the unbounded downstream region, converging to a uniform velocity state at infinity, and a C1,α multidimensional transonic shock separating the subsonic flow from the supersonic upstream flow; the uniform velocity state at the exit at infinity in the downstream direction is uniquely determined by the supersonic upstream flow; and the shock is orthogonal to the nozzle boundary at every point of their intersection. In order to construct such a transonic flow, we reformulate the multidimensional transonic nozzle problem into a free boundary problem for the subsonic phase, in which the equation is elliptic and the free boundary is a transonic shock. The free boundary conditions are determined by the Rankine–Hugoniot conditions along the shock. We further develop a nonlinear iteration approach and employ its advantages to deal with such a free boundary problem in the unbounded domain. We also prove that the transonic flow with a transonic shock is unique and stable with respect to the nozzle boundary and the smooth supersonic upstream flow at the entrance. © Springer-Verlag 2006 |
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Abstract We establish the existence and stability of multidimensional steady transonic flows with transonic shocks through an infinite nozzle of arbitrary cross-sections, including a slowly varying de Laval nozzle. The transonic flow is governed by the inviscid potential flow equation with supersonic upstream flow at the entrance, uniform subsonic downstream flow at the exit at infinity, and the slip boundary condition on the nozzle boundary. Our results indicate that, if the supersonic upstream flow at the entrance is sufficiently close to a uniform flow, there exists a solution that consists of a C1,α subsonic flow in the unbounded downstream region, converging to a uniform velocity state at infinity, and a C1,α multidimensional transonic shock separating the subsonic flow from the supersonic upstream flow; the uniform velocity state at the exit at infinity in the downstream direction is uniquely determined by the supersonic upstream flow; and the shock is orthogonal to the nozzle boundary at every point of their intersection. In order to construct such a transonic flow, we reformulate the multidimensional transonic nozzle problem into a free boundary problem for the subsonic phase, in which the equation is elliptic and the free boundary is a transonic shock. The free boundary conditions are determined by the Rankine–Hugoniot conditions along the shock. We further develop a nonlinear iteration approach and employ its advantages to deal with such a free boundary problem in the unbounded domain. We also prove that the transonic flow with a transonic shock is unique and stable with respect to the nozzle boundary and the smooth supersonic upstream flow at the entrance. © Springer-Verlag 2006 |
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Abstract We establish the existence and stability of multidimensional steady transonic flows with transonic shocks through an infinite nozzle of arbitrary cross-sections, including a slowly varying de Laval nozzle. The transonic flow is governed by the inviscid potential flow equation with supersonic upstream flow at the entrance, uniform subsonic downstream flow at the exit at infinity, and the slip boundary condition on the nozzle boundary. Our results indicate that, if the supersonic upstream flow at the entrance is sufficiently close to a uniform flow, there exists a solution that consists of a C1,α subsonic flow in the unbounded downstream region, converging to a uniform velocity state at infinity, and a C1,α multidimensional transonic shock separating the subsonic flow from the supersonic upstream flow; the uniform velocity state at the exit at infinity in the downstream direction is uniquely determined by the supersonic upstream flow; and the shock is orthogonal to the nozzle boundary at every point of their intersection. In order to construct such a transonic flow, we reformulate the multidimensional transonic nozzle problem into a free boundary problem for the subsonic phase, in which the equation is elliptic and the free boundary is a transonic shock. The free boundary conditions are determined by the Rankine–Hugoniot conditions along the shock. We further develop a nonlinear iteration approach and employ its advantages to deal with such a free boundary problem in the unbounded domain. We also prove that the transonic flow with a transonic shock is unique and stable with respect to the nozzle boundary and the smooth supersonic upstream flow at the entrance. © Springer-Verlag 2006 |
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