A novel fully-implicit finite volume method applied to the lid-driven cavity problem-Part II: Linear stability analysis

A novel finite volume method, described in Part I of this paper (Sahin and Owens, Int. J. Numer. Meth. Fluids 2003; 42:57–77), is applied in the linear stability analysis of a lid‐driven cavity flow in a square enclosure. A combination of Arnoldi's method and extrapolation to zero mesh size all...

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Vydáno v:	International journal for numerical methods in fluids Ročník 42; číslo 1; s. 79 - 88
Hlavní autoři:	Sahin, Mehmet, Owens, Robert G.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Chichester, UK John Wiley & Sons, Ltd 10.05.2003 Wiley
Témata:	Computational methods in fluid dynamics Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) implicit finite volume methods Laminar flows Laminar flows in cavities lid-driven cavity flow linear stability Physics Stability of laminar flows Streamlines Computational fluid dynamics Digital simulation Vorticity Linear stability Unsteady flow Incompressible fluid Hopf bifurcation Cavity flow Finite volume methods Turbulent laminar transition Moving wall
ISSN:	0271-2091, 1097-0363
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Abstract	A novel finite volume method, described in Part I of this paper (Sahin and Owens, Int. J. Numer. Meth. Fluids 2003; 42:57–77), is applied in the linear stability analysis of a lid‐driven cavity flow in a square enclosure. A combination of Arnoldi's method and extrapolation to zero mesh size allows us to determine the first critical Reynolds number at which Hopf bifurcation takes place. The extreme sensitivity of the predicted critical Reynolds number to the accuracy of the method and to the treatment of the singularity points is noted. Results are compared with those in the literature and are in very good agreement. Copyright © 2003 John Wiley & Sons, Ltd.
AbstractList	A novel finite volume method, described in Part I of this paper (Sahin and Owens, Int. J. Numer. Meth. Fluids 2003; 42:57–77), is applied in the linear stability analysis of a lid‐driven cavity flow in a square enclosure. A combination of Arnoldi's method and extrapolation to zero mesh size allows us to determine the first critical Reynolds number at which Hopf bifurcation takes place. The extreme sensitivity of the predicted critical Reynolds number to the accuracy of the method and to the treatment of the singularity points is noted. Results are compared with those in the literature and are in very good agreement. Copyright © 2003 John Wiley & Sons, Ltd. A novel finite volume method, described in Part I of this paper (Sahin and Owens, Int. J. Numer. Meth. Fluids 2003; 42 :57–77), is applied in the linear stability analysis of a lid‐driven cavity flow in a square enclosure. A combination of Arnoldi's method and extrapolation to zero mesh size allows us to determine the first critical Reynolds number at which Hopf bifurcation takes place. The extreme sensitivity of the predicted critical Reynolds number to the accuracy of the method and to the treatment of the singularity points is noted. Results are compared with those in the literature and are in very good agreement. Copyright © 2003 John Wiley & Sons, Ltd.
Author	Owens, Robert G. Sahin, Mehmet
Author_xml	– sequence: 1 givenname: Mehmet surname: Sahin fullname: Sahin, Mehmet organization: FSTI-ISE-LMF, Ecole Polytechnique Fédérale de Lausanne, CH 1015 Lausanne, Switzerland – sequence: 2 givenname: Robert G. surname: Owens fullname: Owens, Robert G. email: robert.owens@effl.ch organization: FSTI-ISE-LMF, Ecole Polytechnique Fédérale de Lausanne, CH 1015 Lausanne, Switzerland
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Keywords	Streamlines Computational fluid dynamics Digital simulation Vorticity Linear stability Unsteady flow Incompressible fluid Hopf bifurcation Cavity flow Finite volume methods Turbulent laminar transition Moving wall
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References_xml	– reference: Goodrich JW, Gustafson K, Halasi K. Hopf bifurcation in the driven cavity. Journal of Computational Physics 1990; 90(1):219-261. – reference: Sahin M, Owens RG. A novel fully-implicit finite volume method applied to the lid-driven cavity problem. Part I. High Reynolds number flow calculations. International Journal for Numerical Methods in Fluids 2003; 42:57-77. – reference: Shankar PN, Deshpande MD. Fluid mechanics in the driven cavity. Annual Review of Fluid Mechanics 2000; 32:93-136. – reference: Botella O. On the solution of the Navier-Stokes equations using Chebyshev projection schemes with third-order accuracy in time. Computers & Fluids 1997; 26(2):107-116. – reference: Leriche E, Deville MO. A Uzawa-type pressure solver for the Lanczos-τ-Chebyshev spectral method. Computers & Fluids 2003; submitted. – reference: Poliashenko M, Aidun CK. A direct method for computation of simple bifurcations. Journal of Computational Physics 1995; 121(2):246-260. – reference: Natarajan R. An Arnoldi-based iterative scheme for nonsymmetric matrix pencils arising in finite element stability problems. Journal of Computational Physics 1992; 100(1):128-142. – reference: Kupferman R. A central-difference scheme for a pure stream function formulation of incompressible viscous flow. SIAM Journal on Scientific Computing 2001; 23(1):1-18. – reference: Gervais JJ, Lemelin D, Pierre R. Some experiments with stability analysis of discrete incompressible flows in the lid-driven cavity. International Journal for Numerical Methods in Fluids 1997; 24(5):477-492. – reference: Cazemier W, Verstappen RWCP, Veldman AEP. Proper orthogonal decomposition and low-dimensional models for driven cavity flows. Physics of Fluids 1998; 10(7):1685-1699. – reference: Shen J. Hopf bifurcation of the unsteady regularized driven cavity flow. Journal of Computational Physics 1991; 95(1):228-245. – reference: Batoul A, Khallouf H, Labrosse G. Une méthode de résolution directe (pseudo-spectrale) du problème de Stokes 2D/3D instationnaire. Application à la cavité entrainée carrée. Comptes Rendus de l'Académie des Sciences de Paris 1994; 319(12):1455-1461. – reference: Jennings A. Matrix Computation for Engineers and Scientists. Wiley: London, 1977. – reference: Botella O, Peyret R. Computing singular solutions of the Navier-Stokes equations with the Chebyshev-collocation method. International Journal for Numerical Methods in Fluids 2001; 36(2):125-163. – reference: Saad Y. Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices. Linear Algebra and its Applications 1980; 34:269-295. – reference: Pan TW, Glowinski R. A projection/wave-like equation method for the numerical simulation of incompressible viscous fluid flow modeled by the Navier-Stokes equations. Computational Fluid Dynamics Journal 2000; 9(2):28-42. – reference: Fortin A, Jardak M, Gervais JJ, Pierre R. Localization of Hopf bifurcations in fluid flow problems. International Journal for Numerical Methods in Fluids 1997; 24(11):1185-1210. – reference: Arnoldi WE. The principle of minimized iterations in the solution of the matrix eigenvalue problem. Quarterly of Applied Mathematics 1951; 9:17-29. – volume: 34 start-page: 269 year: 1980 end-page: 295 article-title: Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices publication-title: Linear Algebra and its Applications – volume: 10 start-page: 1685 issue: 7 year: 1998 end-page: 1699 article-title: Proper orthogonal decomposition and low‐dimensional models for driven cavity flows publication-title: Physics of Fluids – volume: 121 start-page: 246 issue: 2 year: 1995 end-page: 260 article-title: A direct method for computation of simple bifurcations publication-title: Journal of Computational Physics – volume: 26 start-page: 107 issue: 2 year: 1997 end-page: 116 article-title: On the solution of the Navier‐Stokes equations using Chebyshev projection schemes with third‐order accuracy in time publication-title: Computers & Fluids – volume: 42 start-page: 57 year: 2003 end-page: 77 article-title: A novel fully‐implicit finite volume method applied to the lid‐driven cavity problem. Part I. High Reynolds number flow calculations publication-title: International Journal for Numerical Methods in Fluids – volume: 95 start-page: 228 issue: 1 year: 1991 end-page: 245 article-title: Hopf bifurcation of the unsteady regularized driven cavity flow publication-title: Journal of Computational Physics – volume: 32 start-page: 93 year: 2000 end-page: 136 article-title: Fluid mechanics in the driven cavity publication-title: Annual Review of Fluid Mechanics – volume: 319 start-page: 1455 issue: 12 year: 1994 end-page: 1461 article-title: Une méthode de résolution directe (pseudo‐spectrale) du problème de Stokes 2D/3D instationnaire. Application à la cavité entrainée carrée publication-title: Comptes Rendus de l'Académie des Sciences de Paris – volume: 24 start-page: 477 issue: 5 year: 1997 end-page: 492 article-title: Some experiments with stability analysis of discrete incompressible flows in the lid‐driven cavity publication-title: International Journal for Numerical Methods in Fluids – volume: 9 start-page: 17 year: 1951 end-page: 29 article-title: The principle of minimized iterations in the solution of the matrix eigenvalue problem publication-title: Quarterly of Applied Mathematics – volume: 23 start-page: 1 issue: 1 year: 2001 end-page: 18 article-title: A central‐difference scheme for a pure stream function formulation of incompressible viscous flow publication-title: SIAM Journal on Scientific Computing – volume: 24 start-page: 1185 issue: 11 year: 1997 end-page: 1210 article-title: Localization of Hopf bifurcations in fluid flow problems publication-title: International Journal for Numerical Methods in Fluids – volume: 9 start-page: 28 issue: 2 year: 2000 end-page: 42 article-title: A projection/wave‐like equation method for the numerical simulation of incompressible viscous fluid flow modeled by the Navier‐Stokes equations publication-title: Computational Fluid Dynamics Journal – volume: 36 start-page: 125 issue: 2 year: 2001 end-page: 163 article-title: Computing singular solutions of the Navier‐Stokes equations with the Chebyshev‐collocation method publication-title: International Journal for Numerical Methods in Fluids – volume: 90 start-page: 219 issue: 1 year: 1990 end-page: 261 article-title: Hopf bifurcation in the driven cavity publication-title: Journal of Computational Physics – year: 2003 article-title: A Uzawa‐type pressure solver for the Lanczos‐τ‐Chebyshev spectral method publication-title: Computers & Fluids – volume: 100 start-page: 128 issue: 1 year: 1992 end-page: 142 article-title: An Arnoldi‐based iterative scheme for nonsymmetric matrix pencils arising in finite element stability problems publication-title: Journal of Computational Physics – year: 1977 – volume: 9 start-page: 28 issue: 2 year: 2000 ident: e_1_2_1_9_2 article-title: A projection/wave‐like equation method for the numerical simulation of incompressible viscous fluid flow modeled by the Navier‐Stokes equations publication-title: Computational Fluid Dynamics Journal – ident: e_1_2_1_13_2 doi: 10.1002/(SICI)1097-0363(19970315)24:5<477::AID-FLD500>3.0.CO;2-S – ident: e_1_2_1_10_2 doi: 10.1137/S1064827500373395 – ident: e_1_2_1_7_2 doi: 10.1002/(SICI)1097-0363(19970615)24:11<1185::AID-FLD535>3.0.CO;2-X – ident: e_1_2_1_16_2 doi: 10.1002/fld.442 – ident: e_1_2_1_17_2 doi: 10.1090/qam/42792 – ident: e_1_2_1_5_2 doi: 10.1016/S0045-7930(96)00032-1 – volume: 319 start-page: 1455 issue: 12 year: 1994 ident: e_1_2_1_4_2 article-title: Une méthode de résolution directe (pseudo‐spectrale) du problème de Stokes 2D/3D instationnaire. Application à la cavité entrainée carrée publication-title: Comptes Rendus de l'Académie des Sciences de Paris – ident: e_1_2_1_14_2 doi: 10.1063/1.869686 – ident: e_1_2_1_2_2 doi: 10.1146/annurev.fluid.32.1.93 – ident: e_1_2_1_15_2 doi: 10.1016/0021-9991(90)90204-E – ident: e_1_2_1_19_2 doi: 10.1016/0021-9991(92)90315-P – volume-title: Matrix Computation for Engineers and Scientists year: 1977 ident: e_1_2_1_6_2 – year: 2003 ident: e_1_2_1_8_2 article-title: A Uzawa‐type pressure solver for the Lanczos‐τ‐Chebyshev spectral method publication-title: Computers & Fluids – ident: e_1_2_1_18_2 doi: 10.1016/0024-3795(80)90169-X – ident: e_1_2_1_12_2 doi: 10.1016/S0021-9991(95)90068-3 – ident: e_1_2_1_11_2 doi: 10.1002/fld.121 – ident: e_1_2_1_3_2 doi: 10.1016/0021-9991(91)90261-I
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Snippet	A novel finite volume method, described in Part I of this paper (Sahin and Owens, Int. J. Numer. Meth. Fluids 2003; 42:57–77), is applied in the linear... A novel finite volume method, described in Part I of this paper (Sahin and Owens, Int. J. Numer. Meth. Fluids 2003; 42 :57–77), is applied in the linear...
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SubjectTerms	Computational methods in fluid dynamics Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) implicit finite volume methods Laminar flows Laminar flows in cavities lid-driven cavity flow linear stability Physics Stability of laminar flows
Title	A novel fully-implicit finite volume method applied to the lid-driven cavity problem-Part II: Linear stability analysis
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