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Volumn 83, Issue 1, 2003, Pages 3-25

Asymptotic based preconditioning technique for low Mach number flows

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EID: 21144456086     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.200310002     Document Type: Review
Times cited : (13)

References (80)
  • 2
    • 0012281253 scopus 로고
    • On the incompressible limit of the compressible Euler equations
    • K. Asano, On the incompressible limit of the compressible Euler equations, Japan J. Appl. Math. 4, 455-488 (1987).
    • (1987) Japan J. Appl. Math. , vol.4 , pp. 455-488
    • Asano, K.1
  • 4
    • 0003241715 scopus 로고
    • The design and application of upwind schemes on unstructured meshes
    • T. J. Barth and D. C. Jesperson, The design and application of upwind schemes on unstructured meshes, AIAA paper 89-0366 (1989).
    • (1989) AIAA Paper , vol.89 , Issue.366
    • Barth, T.J.1    Jesperson, D.C.2
  • 5
    • 0020842331 scopus 로고
    • A low Mach number Euler formulation and application to timeiIterative LBI schemes
    • W. R. Briley, H. McDonald, and S. J. Shamroth, A low Mach number Euler formulation and application to timeiIterative LBI schemes, AIAA J. 21, 1467-1469 (1983).
    • (1983) AIAA J. , vol.21 , pp. 1467-1469
    • Briley, W.R.1    McDonald, H.2    Shamroth, S.J.3
  • 6
    • 28144434245 scopus 로고
    • The application of preconditioning in viscous flows
    • D. Choi and C. L. Merkle, The application of preconditioning in viscous flows, J. Comput. Phys. 105, 207-223 (1993).
    • (1993) J. Comput. Phys. , vol.105 , pp. 207-223
    • Choi, D.1    Merkle, C.L.2
  • 7
    • 40449093496 scopus 로고
    • A numerical method for solving incompressible viscous flow problems
    • A. J. Chorin, A numerical method for solving incompressible viscous flow problems, J. Comput. Phys. 2, 12-26 (1967).
    • (1967) J. Comput. Phys. , vol.2 , pp. 12-26
    • Chorin, A.J.1
  • 9
    • 0001484343 scopus 로고    scopus 로고
    • Weighted essential non-oscillatory schemes for the interpolation of mean values on unstructured grids
    • O. Friedrich, Weighted essential non-oscillatory schemes for the interpolation of mean values on unstructured grids, J. Comput. Phys. 144, 194-212 (1998).
    • (1998) J. Comput. Phys. , vol.144 , pp. 194-212
    • Friedrich, O.1
  • 13
    • 0000935267 scopus 로고
    • A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics
    • S. K. Godunov, A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics, Mat. Sb. 47, 357-393 (1959).
    • (1959) Mat. Sb. , vol.47 , pp. 357-393
    • Godunov, S.K.1
  • 14
    • 0344389046 scopus 로고    scopus 로고
    • On the behaviour of upwind schemes in the low Mach number limit
    • H. Guillard and C. Viozat, On the behaviour of upwind schemes in the low Mach number limit, Comput. Fluids 28, 63-86 (1999).
    • (1999) Comput. Fluids , vol.28 , pp. 63-86
    • Guillard, H.1    Viozat, C.2
  • 16
    • 4244076985 scopus 로고
    • An implicit flux-vector splitting scheme for the computation of viscous hypersonic flow
    • D. Hänel and R. Schwane, An implicit flux-vector splitting scheme for the computation of viscous hypersonic flow, AIAA Paper 89-0274 (1989).
    • (1989) AIAA Paper , vol.89 , Issue.274
    • Hänel, D.1    Schwane, R.2
  • 17
    • 5544234042 scopus 로고
    • On the accuracy of upwind schemes for the solution of the navier-stokes equations
    • D. Hänel, R. Schwane, and G. Seider, On the accuracy of upwind schemes for the solution of the navier-stokes equations, AIAA Paper 87-1105 (1987).
    • (1987) AIAA Paper , vol.87 , Issue.1105
    • Hänel, D.1    Schwane, R.2    Seider, G.3
  • 19
    • 0002237548 scopus 로고
    • Dynamic adaptivity and residual control in unsteady compressible flow computation
    • V. Hannemann, D. Hempel, and Th. Sonar, Dynamic adaptivity and residual control in unsteady compressible flow computation, Math. Comput. Model. 20, 201-213 (1994).
    • (1994) Math. Comput. Model. , vol.20 , pp. 201-213
    • Hannemann, V.1    Hempel, D.2    Sonar, T.3
  • 20
    • 0031926098 scopus 로고    scopus 로고
    • A comparative study of different sets of variables for solving compressible and incompressible flows
    • G. Hauke and T. J. R. Hughes, A comparative study of different sets of variables for solving compressible and incompressible flows, Comput. Methods Appl. Mech. Eng. 153, 1-44 (1998).
    • (1998) Comput. Methods Appl. Mech. Eng. , vol.153 , pp. 1-44
    • Hauke, G.1    Hughes, T.J.R.2
  • 22
    • 21444436868 scopus 로고    scopus 로고
    • On the comparison of four different implementations of an third-order ENO scheme of box type for the computation of compressible flow
    • C. Hietel, A. Meister, and Th. Sonar, On the comparison of four different implementations of an third-order ENO scheme of box type for the computation of compressible flow, Numer. Algorithms 13, 77-105 (1996).
    • (1996) Numer. Algorithms , vol.13 , pp. 77-105
    • Hietel, C.1    Meister, A.2    Sonar, Th.3
  • 26
    • 0343140269 scopus 로고    scopus 로고
    • A numerical scheme for low mach number flow based on asymptotic analysis with time-dependent adaptation of the asymptotic sequence
    • edited by C. Hirsch and M. Pandolfi, Athens
    • L. Hoffmann and A. Meister, A numerical scheme for low mach number flow based on asymptotic analysis with time-dependent adaptation of the asymptotic sequence, in: Proc. 4th ECCOMAS Computational Fluid Dynamics Conference, Vol. 1, Part 1, edited by C. Hirsch and M. Pandolfi, Athens 1998, pp. 567-572.
    • (1998) Proc. 4th ECCOMAS Computational Fluid Dynamics Conference , vol.1 , Issue.1 PART , pp. 567-572
    • Hoffmann, L.1    Meister, A.2
  • 28
    • 0345689581 scopus 로고    scopus 로고
    • A compressible low mach number scheme based on image processing and asymptotic analysis
    • L. Hoffmann and A. Meister, A compressible low mach number scheme based on image processing and asymptotic analysis, Comput. Fluid Dynamics J. 9, 399-410 (2001).
    • (2001) Comput. Fluid Dynamics J. , vol.9 , pp. 399-410
    • Hoffmann, L.1    Meister, A.2
  • 29
    • 0003140474 scopus 로고    scopus 로고
    • Weighted essentially non-oscillatory schemes on triangular meshes
    • C. Hu and C.-W. Shu, Weighted essentially non-oscillatory schemes on triangular meshes, J. Comput. Phys. 150, 97-127 (1999).
    • (1999) J. Comput. Phys. , vol.150 , pp. 97-127
    • Hu, C.1    Shu, C.-W.2
  • 30
    • 84990587387 scopus 로고
    • Computational transonics
    • A. Jameson, Computational transonics, Comm. Pure Appl. Math. 41, 507-549 (1988).
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 507-549
    • Jameson, A.1
  • 32
    • 84980156074 scopus 로고
    • Singular limits of quasilinear hyperbolic system with large parameters and the incompressible limit of compressible fluids
    • S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic system with large parameters and the incompressible limit of compressible fluids, Comm. Pure Appl. Math. 34, 481-524 (1981).
    • (1981) Comm. Pure Appl. Math. , vol.34 , pp. 481-524
    • Klainerman, S.1    Majda, A.2
  • 33
    • 84990557419 scopus 로고
    • Compressible and incompressible fluids
    • S. Klainerman and A. Majda, Compressible and incompressible fluids, Comm. Pure Appl. Math. 35, 629-651 (1982).
    • (1982) Comm. Pure Appl. Math. , vol.35 , pp. 629-651
    • Klainerman, S.1    Majda, A.2
  • 34
    • 0000578716 scopus 로고
    • Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics. I: One-dimensional flow
    • R. Klein, Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics. I: One-dimensional flow, J. Comput. Phys. 121, 213-237 (1995).
    • (1995) J. Comput. Phys. , vol.121 , pp. 213-237
    • Klein, R.1
  • 36
    • 0023602048 scopus 로고
    • Solution of two-dimensional Euler equations - Experience with a finite volume code
    • Deutsche Forschungsund Versuchsanstalt für Luft- und Raumfahrt DFVLR, Köln
    • N. Kroll, R. K. Jain, Solution of two-dimensional Euler equations - Experience with a finite volume code, Deutsche Forschungsund Versuchsanstalt für Luft- und Raumfahrt DFVLR, Forschungsbericht FB 87-41, Köln (1987).
    • (1987) Forschungsbericht , vol.FB 87-41
    • Kroll, N.1    Jain, R.K.2
  • 39
    • 0033098692 scopus 로고    scopus 로고
    • Convexity rule for shape decomposition based on discrete contour evolution
    • L. J. Latecki and R. Lakämper, Convexity rule for shape decomposition based on discrete contour evolution, Comput. Vision Image Understanding 73(3), 441-454 (1999).
    • (1999) Comput. Vision Image Understanding , vol.73 , Issue.3 , pp. 441-454
    • Latecki, L.J.1    Lakämper, R.2
  • 42
    • 0342550031 scopus 로고
    • also in J. Comput. Phys. 107, 23-39 (1993).
    • (1993) J. Comput. Phys. , vol.107 , pp. 23-39
  • 43
    • 0040521849 scopus 로고
    • Development of an implicit finite volume scheme for the computation of unsteady flow fields on unstructured moving grids
    • edited by K.W. Morton and M.J. Baines (Oxford, Clarendon Press)
    • A. Meister, Development of an implicit finite volume scheme for the computation of unsteady flow fields on unstructured moving grids, in: Numerical Methods for Fluid Dynamics V. Vol. V, edited by K.W. Morton and M.J. Baines (Oxford, Clarendon Press, 1995), pp. 481-488.
    • (1995) Numerical Methods for Fluid Dynamics V , vol.5 , pp. 481-488
    • Meister, A.1
  • 45
    • 0038631385 scopus 로고    scopus 로고
    • Comparison of different Krylov subspace methods embedded in an implicit finite volume scheme for the computation of viscous and inviscid flow fields on unstructured grids
    • A. Meister, Comparison of different Krylov subspace methods embedded in an implicit finite volume scheme for the computation of viscous and inviscid flow fields on unstructured grids, J. Comput. Phys. 140, 311-345 (1998).
    • (1998) J. Comput. Phys. , vol.140 , pp. 311-345
    • Meister, A.1
  • 46
    • 0343193151 scopus 로고    scopus 로고
    • Asymptotic single and multiple scale expansions in the low Mach number limit
    • A. Meister, Asymptotic single and multiple scale expansions in the low Mach number limit, SIAM J. Appl. Math. 60(1), 256-271 (1999).
    • (1999) SIAM J. Appl. Math. , vol.60 , Issue.1 , pp. 256-271
    • Meister, A.1
  • 49
    • 0040521848 scopus 로고    scopus 로고
    • Computation of laminar and turbulent compressible flow fields on unstructured grids with an implicit finite volume scheme
    • Prague
    • A. Meister and M. Oevermann, Computation of laminar and turbulent compressible flow fields on unstructured grids with an implicit finite volume scheme, in: Proc. 2nd Seminar on Euler and Navier-Stokes Equations, Prague 1996.
    • (1996) Proc. 2nd Seminar on Euler and Navier-stokes Equations
    • Meister, A.1    Oevermann, M.2
  • 50
    • 22444452405 scopus 로고    scopus 로고
    • An implicit finite volume approach of the k - ε turbulence model on unstructured grids
    • A. Meister and M. Oevermann, An implicit finite volume approach of the k - ε turbulence model on unstructured grids, ZAMM 78(11), 743-757 (1998).
    • (1998) ZAMM , vol.78 , Issue.11 , pp. 743-757
    • Meister, A.1    Oevermann, M.2
  • 51
    • 0013079330 scopus 로고    scopus 로고
    • Finite-volume schemes for compressible fluid flow
    • A. Meister and Th. Sonar, Finite-volume schemes for compressible fluid flow, Surv. Math. Ind. 8, 1-36 (1998).
    • (1998) Surv. Math. Ind. , vol.8 , pp. 1-36
    • Meister, A.1    Sonar, Th.2
  • 52
    • 0035645930 scopus 로고    scopus 로고
    • Efficient preconditioning of linear systems arising from the discretization of hyperbolic conservation laws
    • A. Meister and C. Vömel, Efficient preconditioning of linear systems arising from the discretization of hyperbolic conservation laws, Advances Comput. Math. 14(1), 49-73 (2001).
    • (2001) Advances Comput. Math. , vol.14 , Issue.1 , pp. 49-73
    • Meister, A.1    Vömel, C.2
  • 53
    • 0023360166 scopus 로고
    • Computation of low-speed compressible flows with heat addition
    • C. L. Merkle and Y.-H. Choi, Computation of low-speed compressible flows with heat addition, AIAA J. 25(6), 831-838 (1987).
    • (1987) AIAA J. , vol.25 , Issue.6 , pp. 831-838
    • Merkle, C.L.1    Choi, Y.-H.2
  • 54
    • 0024034697 scopus 로고
    • Computation of low-speed compressible flows with time-marching procedure
    • C. L. Merkle and Y.-H. Choi, Computation of low-speed compressible flows with time-marching procedure, Int. J. Num. Meth. Eng. 25, 293-311 (1988).
    • (1988) Int. J. Num. Meth. Eng. , vol.25 , pp. 293-311
    • Merkle, C.L.1    Choi, Y.-H.2
  • 55
    • 84968510942 scopus 로고
    • Upwind schemes for hyperbolic systems of conservation laws
    • S. Osher and F. Solomon, Upwind schemes for hyperbolic systems of conservation laws, Math. Comput. 38, 339-377 (1982).
    • (1982) Math. Comput. , vol.38 , pp. 339-377
    • Osher, S.1    Solomon, F.2
  • 56
    • 0004025930 scopus 로고
    • A contribution to the great Riemann solver debate
    • Hampton, Virginia
    • J. J. Quirk, A contribution to the great Riemann solver debate, ICASE Report 92-64, Hampton, Virginia (1992).
    • (1992) ICASE Report , vol.92 , Issue.64
    • Quirk, J.J.1
  • 58
    • 2942757053 scopus 로고
    • Approximate Riemann solvers, parameter vectors, and difference schemes
    • P. L. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys. 43, 357-372 (1981).
    • (1981) J. Comput. Phys. , vol.43 , pp. 357-372
    • Roe, P.L.1
  • 60
    • 0000880485 scopus 로고    scopus 로고
    • Semi-implicit extension of a godunov-type compressible solver based on Low Mach Number Asymptotics. II. Multi-dimesional, variable density zero Mach number flow
    • T. Schneider, N. Botta, K. J. Geratz, and R. Klein, Semi-implicit extension of a godunov-type compressible solver based on Low Mach Number Asymptotics. II. Multi-dimesional, variable density zero Mach number flow, J. Comput. Phys. 155, 248-286 (1999).
    • (1999) J. Comput. Phys. , vol.155 , pp. 248-286
    • Schneider, T.1    Botta, N.2    Geratz, K.J.3    Klein, R.4
  • 63
    • 45449125925 scopus 로고
    • Efficient implementation of essentially nonoscillatory shock-capturing schemes
    • C.-W. Shu and S. Osher, Efficient implementation of essentially nonoscillatory shock-capturing schemes, J. Comput. Phys. 77, 439-471 (1988).
    • (1988) J. Comput. Phys. , vol.77 , pp. 439-471
    • Shu, C.-W.1    Osher, S.2
  • 64
    • 0001358722 scopus 로고
    • A coupled implicit method for chemical non-equilibrium flows at all speeds
    • J.-S. Shuen, K.-H. Chen, and Y. Choi, A coupled implicit method for chemical non-equilibrium flows at all speeds, J. Comput. Phys. 106, 306-318 (1993).
    • (1993) J. Comput. Phys. , vol.106 , pp. 306-318
    • Shuen, J.-S.1    Chen, K.-H.2    Choi, Y.3
  • 65
    • 0039929025 scopus 로고
    • On the design of an upwind scheme for compressible flow on general triangulations
    • Th. Sonar, On the design of an upwind scheme for compressible flow on general triangulations, Numer. Algorithms 4, 135-149 (1993).
    • (1993) Numer. Algorithms , vol.4 , pp. 135-149
    • Sonar, Th.1
  • 67
    • 33748509895 scopus 로고    scopus 로고
    • Private communication
    • E. Stanewsky, Private communication (1999)
    • (1999)
    • Stanewsky, E.1
  • 68
    • 0004026131 scopus 로고
    • Airfoil SKF 1.1 with maneuver flap
    • E. Stanewsky and J. J. Thibert, Airfoil SKF 1.1 with maneuver flap. AGARD AR 138, A5-1-A5-29 (1979).
    • (1979) AGARD AR , vol.138
    • Stanewsky, E.1    Thibert, J.J.2
  • 69
    • 49049151571 scopus 로고
    • Flux vector splitting of the inviscid gasdynamic equations with application to finite-differnce methods
    • J. L. Steger and R. F. Warming, Flux vector splitting of the inviscid gasdynamic equations with application to finite-differnce methods, J. Comput. Phys. 40, 263-293 (1981).
    • (1981) J. Comput. Phys. , vol.40 , pp. 263-293
    • Steger, J.L.1    Warming, R.F.2
  • 72
    • 45949116154 scopus 로고
    • Preconditioned methods for solving the incompressible and low speed compressible equations
    • E. Turkel, Preconditioned methods for solving the incompressible and low speed compressible equations, J. Comput. Phys. 72, 277-298 (1987).
    • (1987) J. Comput. Phys. , vol.72 , pp. 277-298
    • Turkel, E.1
  • 73
    • 0000570341 scopus 로고
    • The incompressible limit and the initial layer of the compressible Euler equations
    • S. Ukai, The incompressible limit and the initial layer of the compressible Euler equations, J. Math. Kyoto Univ. 26, 323-331 (1986).
    • (1986) J. Math. Kyoto Univ. , vol.26 , pp. 323-331
    • Ukai, S.1
  • 74
    • 0000005482 scopus 로고
    • BI-CGSTAB: A fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems
    • H. A. van der Vorst, BI-CGSTAB: A fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Stat. Comput. 13, 631-644 (1992).
    • (1992) SIAM J. Sci. Stat. Comput. , vol.13 , pp. 631-644
    • Van Der Vorst, H.A.1
  • 75
    • 0000712325 scopus 로고
    • Flux-vector splitting for the Euler equations
    • edited by E. Krause (Springer, Berlin)
    • B. van Leer, Flux-vector splitting for the Euler equations, in: 8th Internat. Conf. Numer. Methods in Fluid Dynamics, edited by E. Krause (Springer, Berlin, 1982).
    • (1982) 8th Internat. Conf. Numer. Methods in Fluid Dynamics
    • Van Leer, B.1
  • 76
    • 0001349565 scopus 로고    scopus 로고
    • A multigrid semi-implicit line-method for viscous incompressible and low-Mach-number flows on high aspect ratio grids
    • J. Vierendeels, K. Riemslagh, and E. Dick, A multigrid semi-implicit line-method for viscous incompressible and low-Mach-number flows on high aspect ratio grids, J. Comput. Phys. 154, 310-341 (1999).
    • (1999) J. Comput. Phys. , vol.154 , pp. 310-341
    • Vierendeels, J.1    Riemslagh, K.2    Dick, E.3
  • 77
    • 0027187095 scopus 로고
    • Performance of compressible flow codes at low Mach numbers
    • G. Volpe, Performance of compressible flow codes at low Mach numbers. AIAA J. 31(1), 49-56 (1993).
    • (1993) AIAA J. , vol.31 , Issue.1 , pp. 49-56
    • Volpe, G.1
  • 78
    • 0003215906 scopus 로고
    • A flux splitting scheme with high-resolution and robustness for discontinuities
    • Y. Wada and M.-S. Liou, A flux splitting scheme with high-resolution and robustness for discontinuities, AIAA Paper 94-0083 (1994).
    • (1994) AIAA Paper , vol.94 , Issue.83
    • Wada, Y.1    Liou, M.-S.2
  • 80
    • 0029511474 scopus 로고
    • Preconditioning applied to variable and constant density flows
    • J. M. Weiss and W. A. Smith, Preconditioning applied to variable and constant density flows, AIAA J. 33(11), 2050-2057 (1995).
    • (1995) AIAA J. , vol.33 , Issue.11 , pp. 2050-2057
    • Weiss, J.M.1    Smith, W.A.2


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