메뉴 건너뛰기




Volumn 229, Issue 3, 2010, Pages 541-560

A preconditioned Krylov technique for global hydrodynamic stability analysis of large-scale compressible flows

Author keywords

Cayley transformation; Compressible flow; Direct numerical simulation; Hydrodynamic stability; Jacobian free framework; Krylov methods

Indexed keywords

DIRECT NUMERICAL SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; GRAPH DATABASES; HYDRODYNAMICS; ITERATIVE METHODS; MATHEMATICAL TRANSFORMATIONS; NUMERICAL METHODS; NUMERICAL MODELS; STABILITY; TENSORS;

EID: 70449707087     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.09.019     Document Type: Article
Times cited : (54)

References (52)
  • 1
    • 0030215536 scopus 로고    scopus 로고
    • A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems
    • Adams N.A., and Shariff K. A high-resolution hybrid compact-ENO scheme for shock-turbulence interaction problems. J. Comput. Phys. 127 (1996) 27-51
    • (1996) J. Comput. Phys. , vol.127 , pp. 27-51
    • Adams, N.A.1    Shariff, K.2
  • 2
    • 24944533500 scopus 로고    scopus 로고
    • A comparison of eigensolvers for large-scale 3D modal analysis using AMG-preconditioned iterative methods
    • Arbenz P., Hetmaniuk U.L., Lehoucq R.B., and Tuminaro R.S. A comparison of eigensolvers for large-scale 3D modal analysis using AMG-preconditioned iterative methods. Int. J. Numer. Methods Eng. 64 (2005) 204-236
    • (2005) Int. J. Numer. Methods Eng. , vol.64 , pp. 204-236
    • Arbenz, P.1    Hetmaniuk, U.L.2    Lehoucq, R.B.3    Tuminaro, R.S.4
  • 3
    • 84985384413 scopus 로고
    • Progress in the numerical solution of the nonsymmetric eigenvalue problem
    • Bai Z. Progress in the numerical solution of the nonsymmetric eigenvalue problem. Numer. Lin. Alg. Appl. 2 3 (1992) 219-234
    • (1992) Numer. Lin. Alg. Appl. , vol.2 , Issue.3 , pp. 219-234
    • Bai, Z.1
  • 4
    • 84972090823 scopus 로고
    • Discrete modes and continuous spectra in supersonic boundary layers
    • Balakumar P., and Malik M.R. Discrete modes and continuous spectra in supersonic boundary layers. J. Fluid Mech. 239 (1992) 631-656
    • (1992) J. Fluid Mech. , vol.239 , pp. 631-656
    • Balakumar, P.1    Malik, M.R.2
  • 5
    • 0036867930 scopus 로고    scopus 로고
    • Preconditioning techniques for large linear systems: a survey
    • Benzi M. Preconditioning techniques for large linear systems: a survey. J. Comput. Phys. 182 (2002) 418-477
    • (2002) J. Comput. Phys. , vol.182 , pp. 418-477
    • Benzi, M.1
  • 6
    • 0034884436 scopus 로고    scopus 로고
    • Preconditioning highly indefinite and nonsymmetric matrices
    • Benzi M., Haws J.C., and Tu̇ma M. Preconditioning highly indefinite and nonsymmetric matrices. SIAM J. Sci. Comput. 22 (2000) 1333-1353
    • (2000) SIAM J. Sci. Comput. , vol.22 , pp. 1333-1353
    • Benzi, M.1    Haws, J.C.2    Tuma, M.3
  • 7
    • 0014937749 scopus 로고
    • Shear layer instability of an inviscid compressible fluid
    • Blumen W. Shear layer instability of an inviscid compressible fluid. J. Fluid Mech. 40 4 (1970) 769-781
    • (1970) J. Fluid Mech. , vol.40 , Issue.4 , pp. 769-781
    • Blumen, W.1
  • 9
    • 34248546214 scopus 로고    scopus 로고
    • Predicting the onset of flow unsteadiness based on global instability
    • Crouch J.D., Garbaruk A., and Magidov D. Predicting the onset of flow unsteadiness based on global instability. J. Comput. Phys. 224 2 (2007) 924-940
    • (2007) J. Comput. Phys. , vol.224 , Issue.2 , pp. 924-940
    • Crouch, J.D.1    Garbaruk, A.2    Magidov, D.3
  • 12
    • 84966221080 scopus 로고
    • The spectral transformation Lánczos method for the numerical solution of large sparse generalized symmetric eigenvalue problems
    • Ericsson T., and Ruhe A. The spectral transformation Lánczos method for the numerical solution of large sparse generalized symmetric eigenvalue problems. Math. Comput. 35 152 (1980) 1251-1268
    • (1980) Math. Comput. , vol.35 , Issue.152 , pp. 1251-1268
    • Ericsson, T.1    Ruhe, A.2
  • 13
    • 0001031880 scopus 로고
    • A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems
    • Freund R.W. A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems. SIAM J. Sci. Comput. 14 2 (1993) 470-482
    • (1993) SIAM J. Sci. Comput. , vol.14 , Issue.2 , pp. 470-482
    • Freund, R.W.1
  • 15
    • 0012744085 scopus 로고
    • A generalised Cayley transform for the numerical detection of Hopf bifurcations in large systems
    • World Sci. Ser. Appl. Anal. World Sci. Publishing
    • Garratt T.J., Moore G., and Spence A. A generalised Cayley transform for the numerical detection of Hopf bifurcations in large systems. Contributions in Numerical Mathematics vol. 2 (1993), World Sci. Ser. Appl. Anal. World Sci. Publishing 177-195
    • (1993) Contributions in Numerical Mathematics , vol.2 , pp. 177-195
    • Garratt, T.J.1    Moore, G.2    Spence, A.3
  • 16
    • 0031295144 scopus 로고    scopus 로고
    • Spatial instabilities of the incompressible attachment-line flow using sparse matrix Jacobi-Davidson techniques
    • Heeg R.S., and Geurts B.J. Spatial instabilities of the incompressible attachment-line flow using sparse matrix Jacobi-Davidson techniques. Appl. Sci. Res. 59 (1998) 315-329
    • (1998) Appl. Sci. Res. , vol.59 , pp. 315-329
    • Heeg, R.S.1    Geurts, B.J.2
  • 17
    • 0029294282 scopus 로고
    • Direct simulation of evolution and control of three-dimensional instabilities in attachment-line boundary layers
    • Joslin R.D. Direct simulation of evolution and control of three-dimensional instabilities in attachment-line boundary layers. J. Fluid Mech. 291 (1995) 369-392
    • (1995) J. Fluid Mech. , vol.291 , pp. 369-392
    • Joslin, R.D.1
  • 18
    • 68749095988 scopus 로고    scopus 로고
    • BiGlobal stability analysis in curvilinear coordinates of massively separated lifting bodies
    • Kitsios V., Rodriguez D., Theofilis V., Ooi A., and Soria J. BiGlobal stability analysis in curvilinear coordinates of massively separated lifting bodies. J. Comput. Phys. 228 19 (2009) 7181-7196
    • (2009) J. Comput. Phys. , vol.228 , Issue.19 , pp. 7181-7196
    • Kitsios, V.1    Rodriguez, D.2    Theofilis, V.3    Ooi, A.4    Soria, J.5
  • 19
    • 0348198275 scopus 로고    scopus 로고
    • Jacobian-free Newton-Krylov methods: a survey of approaches and applications
    • Knoll D.A., and Keyes D.E. Jacobian-free Newton-Krylov methods: a survey of approaches and applications. J. Comput. Phys. 193 2 (2004) 357-397
    • (2004) J. Comput. Phys. , vol.193 , Issue.2 , pp. 357-397
    • Knoll, D.A.1    Keyes, D.E.2
  • 20
    • 33745597939 scopus 로고    scopus 로고
    • Instabilities in compressible attachment-line boundary layers
    • Le Duc A., Sesterhenn J., and Friedrich R. Instabilities in compressible attachment-line boundary layers. Phys. Fluids 18 044102 (2006)
    • (2006) Phys. Fluids , vol.18 , Issue.044102
    • Le Duc, A.1    Sesterhenn, J.2    Friedrich, R.3
  • 21
    • 0032217348 scopus 로고    scopus 로고
    • Using generalized Cayley transformations within an inexact rational Krylov sequence method
    • (electronic)
    • Lehoucq R.B., and Meerbergen K. Using generalized Cayley transformations within an inexact rational Krylov sequence method. SIAM J. Matrix Anal. Appl. 20 1 (1998) 131-148 (electronic)
    • (1998) SIAM J. Matrix Anal. Appl. , vol.20 , Issue.1 , pp. 131-148
    • Lehoucq, R.B.1    Meerbergen, K.2
  • 22
    • 0035877198 scopus 로고    scopus 로고
    • Large-scale eigenvalue calculations for stability analysis of steady flows on massively parallel computers
    • Lehoucq R.B., and Salinger A.G. Large-scale eigenvalue calculations for stability analysis of steady flows on massively parallel computers. Int. J. Numer. Methods Fluids 36 (2001) 309-327
    • (2001) Int. J. Numer. Methods Fluids , vol.36 , pp. 309-327
    • Lehoucq, R.B.1    Salinger, A.G.2
  • 24
    • 85189839622 scopus 로고    scopus 로고
    • R.B. Lehoucq, D.C. Sorensen, C. Yang, ARPACK Users' Guide. Software, Environments, and Tools. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, 1998.
    • R.B. Lehoucq, D.C. Sorensen, C. Yang, ARPACK Users' Guide. Software, Environments, and Tools. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, 1998.
  • 25
    • 9144220381 scopus 로고
    • Compact finite difference schemes with spectral-like resolution
    • Lele S.K. Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1992) 16-42
    • (1992) J. Comput. Phys. , vol.103 , pp. 16-42
    • Lele, S.K.1
  • 26
    • 85189836947 scopus 로고    scopus 로고
    • Direct numerical simulations of hypersonic flow about a swept parabolic body
    • submitted for publication
    • C.J. Mack, P.J. Schmid, Direct numerical simulations of hypersonic flow about a swept parabolic body. Comput. Fluids (2009), submitted for publication.
    • (2009) Comput. Fluids
    • Mack, C.J.1    Schmid, P.J.2
  • 27
    • 50949104249 scopus 로고    scopus 로고
    • Global stability of swept flow around a parabolic body: connecting attachment-line and crossflow modes
    • Mack C.J., Schmid P.J., and Sesterhenn J.L. Global stability of swept flow around a parabolic body: connecting attachment-line and crossflow modes. J. Fluid Mech. 611 (2008) 205-214
    • (2008) J. Fluid Mech. , vol.611 , pp. 205-214
    • Mack, C.J.1    Schmid, P.J.2    Sesterhenn, J.L.3
  • 29
    • 0031539675 scopus 로고    scopus 로고
    • The restarted Arnoldi method applied to iterative linear system solvers for the computation of rightmost eigenvalues
    • Meerbergen K., and Roose D. The restarted Arnoldi method applied to iterative linear system solvers for the computation of rightmost eigenvalues. SIAM J. Matrix Anal. Appl. 18 1 (1997) 1-20
    • (1997) SIAM J. Matrix Anal. Appl. , vol.18 , Issue.1 , pp. 1-20
    • Meerbergen, K.1    Roose, D.2
  • 30
    • 84958429452 scopus 로고
    • On the inviscid instability of the hyperbolic-tangent velocity profile
    • Michalke A. On the inviscid instability of the hyperbolic-tangent velocity profile. J. Fluid Mech. 19 (1964) 543-556
    • (1964) J. Fluid Mech. , vol.19 , pp. 543-556
    • Michalke, A.1
  • 31
    • 0030353046 scopus 로고    scopus 로고
    • On restarting the Arnoldi method for large non-symmetric eigenvalue problems
    • Morgan R.B. On restarting the Arnoldi method for large non-symmetric eigenvalue problems. Math. Comput. 65 215 (1996) 1213-1230
    • (1996) Math. Comput. , vol.65 , Issue.215 , pp. 1213-1230
    • Morgan, R.B.1
  • 32
    • 0344436092 scopus 로고    scopus 로고
    • Solution of the eigenvalue problems resulting from global non-parallel flow stability analysis
    • Morzynski M., Afanasiev K., and Thiele F. Solution of the eigenvalue problems resulting from global non-parallel flow stability analysis. Comput. Methods Appl. Mech. Eng. 169 (1999) 161-176
    • (1999) Comput. Methods Appl. Mech. Eng. , vol.169 , pp. 161-176
    • Morzynski, M.1    Afanasiev, K.2    Thiele, F.3
  • 33
    • 38049071076 scopus 로고    scopus 로고
    • Effect of discretization order on preconditioning and convergence of a high-order unstructured Newton-GMRES solver for the Euler equations
    • Nejat A., and Ollivier-Gooch C. Effect of discretization order on preconditioning and convergence of a high-order unstructured Newton-GMRES solver for the Euler equations. J. Comput. Phys. 227 (2008) 2366-2386
    • (2008) J. Comput. Phys. , vol.227 , pp. 2366-2386
    • Nejat, A.1    Ollivier-Gooch, C.2
  • 34
    • 0242510000 scopus 로고    scopus 로고
    • On the linear stability of swept attachment-line boundary layer flow. Part 1. Spectrum and asymptotic behaviour
    • Obrist D., and Schmid P.J. On the linear stability of swept attachment-line boundary layer flow. Part 1. Spectrum and asymptotic behaviour. J. Fluid Mech. 493 (2003) 1-29
    • (2003) J. Fluid Mech. , vol.493 , pp. 1-29
    • Obrist, D.1    Schmid, P.J.2
  • 35
    • 70449704702 scopus 로고    scopus 로고
    • A Comparison of Preconditioners for Complex-valued Matrices
    • Technical Report, University of Minnesota Supercomputing Institute Research Report UMSI 2007/139
    • D. Osei-Kuffuor, Y. Saad, A Comparison of Preconditioners for Complex-valued Matrices, Technical Report, University of Minnesota Supercomputing Institute Research Report UMSI 2007/139, 2007.
    • (2007)
    • Osei-Kuffuor, D.1    Saad, Y.2
  • 36
    • 34548174973 scopus 로고    scopus 로고
    • Bifurcations in shock-wave/laminar-boundary layer interaction: global instability approach
    • Robinet J.-C. Bifurcations in shock-wave/laminar-boundary layer interaction: global instability approach. J. Fluid Mech. 579 (2007) 85-112
    • (2007) J. Fluid Mech. , vol.579 , pp. 85-112
    • Robinet, J.-C.1
  • 38
    • 0000048673 scopus 로고
    • GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Saad Y., and Schultz M.H. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7 3 (1986) 856-869
    • (1986) SIAM J. Sci. Stat. Comput. , vol.7 , Issue.3 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 39
    • 0038805681 scopus 로고    scopus 로고
    • Stability and transition of three-dimensional boundary layers
    • Saric W.S., Reed H.L., and White E.B. Stability and transition of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 35 (2003) 413-440
    • (2003) Annu. Rev. Fluid Mech. , vol.35 , pp. 413-440
    • Saric, W.S.1    Reed, H.L.2    White, E.B.3
  • 42
    • 0034258008 scopus 로고    scopus 로고
    • A characteristic-type formulation of the Navier-Stokes equations for high-order upwind schemes
    • Sesterhenn J.L. A characteristic-type formulation of the Navier-Stokes equations for high-order upwind schemes. Comput. Fluids 30 (2001) 37-67
    • (2001) Comput. Fluids , vol.30 , pp. 37-67
    • Sesterhenn, J.L.1
  • 43
    • 0000322706 scopus 로고
    • Implicit application of polynomial filters in a k-step Arnoldi method
    • Sorensen D.C. Implicit application of polynomial filters in a k-step Arnoldi method. SIAM J. Matrix Anal. Appl. 13 1 (1992) 357-385
    • (1992) SIAM J. Matrix Anal. Appl. , vol.13 , Issue.1 , pp. 357-385
    • Sorensen, D.C.1
  • 44
    • 2442500838 scopus 로고    scopus 로고
    • Numerical methods for large eigenvalue problems
    • Sorensen D.C. Numerical methods for large eigenvalue problems. Acta Numer. 11 (2002) 519-584
    • (2002) Acta Numer. , vol.11 , pp. 519-584
    • Sorensen, D.C.1
  • 46
    • 0037403733 scopus 로고    scopus 로고
    • Advances in global linear instability analysis of nonparallel and three-dimensional flows
    • Theofilis V. Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog. Aero. Sci. 39 (2003) 249-315
    • (2003) Prog. Aero. Sci. , vol.39 , pp. 249-315
    • Theofilis, V.1
  • 47
    • 85189838106 scopus 로고    scopus 로고
    • V. Theofilis, T. Colonius, T., 2004. Three-dimensional Instabilities of Compressible Flow Over Open Cavities: Direct Solution of the BiGlobal Eigenvalue Problem, AIAA Paper 2004-2544.
    • V. Theofilis, T. Colonius, T., 2004. Three-dimensional Instabilities of Compressible Flow Over Open Cavities: Direct Solution of the BiGlobal Eigenvalue Problem, AIAA Paper 2004-2544.
  • 48
    • 0042732003 scopus 로고    scopus 로고
    • The extended Görtler-Hämmerlin model for linear instability of three-dimensional incompressible swept attachment-line boundary layer flow
    • Theofilis V., Fedorov A., Obrist D., and Dallmann U.C. The extended Görtler-Hämmerlin model for linear instability of three-dimensional incompressible swept attachment-line boundary layer flow. J. Fluid Mech. 487 (2003) 271-313
    • (2003) J. Fluid Mech. , vol.487 , pp. 271-313
    • Theofilis, V.1    Fedorov, A.2    Obrist, D.3    Dallmann, U.C.4
  • 51
    • 0000005482 scopus 로고
    • Bi-CGSTAB: A fast and smoothly converging variatn of Bi-CG for the solution of non-symmetric linear systems
    • van der Vorst H.A. Bi-CGSTAB: A fast and smoothly converging variatn of Bi-CG for the solution of non-symmetric linear systems. SIAM J. Sci. Statist. Comput. 13 (1992) 631-644
    • (1992) SIAM J. Sci. Statist. Comput. , vol.13 , pp. 631-644
    • van der Vorst, H.A.1
  • 52
    • 85041125685 scopus 로고    scopus 로고
    • Preconditioned Krylov subspace methods for solving nonsymmetric matrices from CFD applications
    • Zhang J. Preconditioned Krylov subspace methods for solving nonsymmetric matrices from CFD applications. Comput. Methods Appl. Mech. Eng. 189 (2000) 825-840
    • (2000) Comput. Methods Appl. Mech. Eng. , vol.189 , pp. 825-840
    • Zhang, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.