Vanishing viscosity method for transonic flow
A vanishing viscosity method is formulated for two-dimensional transonic steady irrotational compressible fluid flows with adiabatic constant γ ∈ [1,3). This formulation allows a family of invariant regions in the phase plane for the corresponding viscous problem, which implies an upper bound unifor...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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2008
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| _version_ | 1797102908164014080 |
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| author | Chen, G Slemrod, M Wang, D |
| author_facet | Chen, G Slemrod, M Wang, D |
| author_sort | Chen, G |
| collection | OXFORD |
| description | A vanishing viscosity method is formulated for two-dimensional transonic steady irrotational compressible fluid flows with adiabatic constant γ ∈ [1,3). This formulation allows a family of invariant regions in the phase plane for the corresponding viscous problem, which implies an upper bound uniformly away from cavitation for the viscous approximate velocity fields. Mathematical entropy pairs are constructed through the Loewner-Morawetz relation via entropy generators governed by a generalized Tricomi equation of mixed elliptic-hyperbolic type, and the corresponding entropy dissipation measures are analyzed so that the viscous approximate solutions satisfy the compensated compactness framework. Then the method of compensated compactness is applied to show that a sequence of solutions to the artificial viscous problem, staying uniformly away from stagnation with uniformly bounded velocity angles, converges to an entropy solution of the inviscid transonic flow problem. © 2008 Springer-Verlag. |
| first_indexed | 2024-03-07T06:12:30Z |
| format | Journal article |
| id | oxford-uuid:f0035429-381e-4cb6-8dcb-1d6d69fbfadc |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:12:30Z |
| publishDate | 2008 |
| record_format | dspace |
| spelling | oxford-uuid:f0035429-381e-4cb6-8dcb-1d6d69fbfadc2022-03-27T11:44:25ZVanishing viscosity method for transonic flowJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:f0035429-381e-4cb6-8dcb-1d6d69fbfadcEnglishSymplectic Elements at Oxford2008Chen, GSlemrod, MWang, DA vanishing viscosity method is formulated for two-dimensional transonic steady irrotational compressible fluid flows with adiabatic constant γ ∈ [1,3). This formulation allows a family of invariant regions in the phase plane for the corresponding viscous problem, which implies an upper bound uniformly away from cavitation for the viscous approximate velocity fields. Mathematical entropy pairs are constructed through the Loewner-Morawetz relation via entropy generators governed by a generalized Tricomi equation of mixed elliptic-hyperbolic type, and the corresponding entropy dissipation measures are analyzed so that the viscous approximate solutions satisfy the compensated compactness framework. Then the method of compensated compactness is applied to show that a sequence of solutions to the artificial viscous problem, staying uniformly away from stagnation with uniformly bounded velocity angles, converges to an entropy solution of the inviscid transonic flow problem. © 2008 Springer-Verlag. |
| spellingShingle | Chen, G Slemrod, M Wang, D Vanishing viscosity method for transonic flow |
| title | Vanishing viscosity method for transonic flow |
| title_full | Vanishing viscosity method for transonic flow |
| title_fullStr | Vanishing viscosity method for transonic flow |
| title_full_unstemmed | Vanishing viscosity method for transonic flow |
| title_short | Vanishing viscosity method for transonic flow |
| title_sort | vanishing viscosity method for transonic flow |
| work_keys_str_mv | AT cheng vanishingviscositymethodfortransonicflow AT slemrodm vanishingviscositymethodfortransonicflow AT wangd vanishingviscositymethodfortransonicflow |