메뉴 건너뛰기




Volumn 230, Issue 17, 2011, Pages 6404-6419

An efficient compact difference scheme for solving the streamfunction formulation of the incompressible Navier-Stokes equations

Author keywords

Compact scheme; Finite difference; Incompressible flow; Navier Stokes equations; Streamfunction formulation

Indexed keywords

FINITE DIFFERENCE METHOD; INCOMPRESSIBLE FLOW; NUMERICAL METHODS; VISCOUS FLOW;

EID: 79959781634     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2010.12.031     Document Type: Article
Times cited : (44)

References (50)
  • 1
    • 84966233568 scopus 로고
    • Multi-level adaptive solutions to boundary-value problems
    • Brandt A. Multi-level adaptive solutions to boundary-value problems. Math. Comput. 1977, 31(138):333-390.
    • (1977) Math. Comput. , vol.31 , Issue.138 , pp. 333-390
    • Brandt, A.1
  • 2
    • 0000350663 scopus 로고
    • High accuracy solution of incompressible Navier-Stokes equations
    • Gupta M.M. High accuracy solution of incompressible Navier-Stokes equations. J. Comput. Phys. 1991, 93:343-359.
    • (1991) J. Comput. Phys. , vol.93 , pp. 343-359
    • Gupta, M.M.1
  • 3
    • 0021207821 scopus 로고
    • A single cell high order scheme for the convection-diffusion equation with variable coefficients
    • Gupta M.M., Manohar R.P., Stephenson J.W. A single cell high order scheme for the convection-diffusion equation with variable coefficients. Int. J. Numer. Methods Fluids 1984, 4:641-651.
    • (1984) Int. J. Numer. Methods Fluids , vol.4 , pp. 641-651
    • Gupta, M.M.1    Manohar, R.P.2    Stephenson, J.W.3
  • 4
    • 49049143188 scopus 로고
    • High Re-solution for incompressible Navier-Stokes equation and a multigrid method
    • Ghia U., Ghia K.N., Shin C.T. High Re-solution for incompressible Navier-Stokes equation and a multigrid method. J. Comput. Phys. 1982, 48:387-411.
    • (1982) J. Comput. Phys. , vol.48 , pp. 387-411
    • Ghia, U.1    Ghia, K.N.2    Shin, C.T.3
  • 5
    • 0002402380 scopus 로고    scopus 로고
    • A conservative finite-volume 2nd order accurate projection method on hybrid unstructured grids
    • Kobayashi M.H., Pereira J.M.C., Pereira J.C.F. A conservative finite-volume 2nd order accurate projection method on hybrid unstructured grids. J. Comput. Phys. 1999, 150:40-75.
    • (1999) J. Comput. Phys. , vol.150 , pp. 40-75
    • Kobayashi, M.H.1    Pereira, J.M.C.2    Pereira, J.C.F.3
  • 6
    • 0029106259 scopus 로고
    • A compact fourth-order finite difference scheme for the incompressible Navier-Stokes equations
    • Li M., Tang T., Fornberg B. A compact fourth-order finite difference scheme for the incompressible Navier-Stokes equations. Int. J. Numer. Methods Fluids 1995, 20:1137-1151.
    • (1995) Int. J. Numer. Methods Fluids , vol.20 , pp. 1137-1151
    • Li, M.1    Tang, T.2    Fornberg, B.3
  • 7
    • 0042696191 scopus 로고    scopus 로고
    • A compact fourth-order finite difference scheme for unsteady viscous incompressible flows
    • Li M., Tang T. A compact fourth-order finite difference scheme for unsteady viscous incompressible flows. J. Sci. Comput. 2001, 16:29-45.
    • (2001) J. Sci. Comput. , vol.16 , pp. 29-45
    • Li, M.1    Tang, T.2
  • 8
    • 0026223011 scopus 로고
    • Differential equation based representtaion of truncation errors for accurate numerical simulation
    • MacKinnon R.J., Johnson R.W. Differential equation based representtaion of truncation errors for accurate numerical simulation. Int. J. Numer. Methods Fluids 1991, 13:739-757.
    • (1991) Int. J. Numer. Methods Fluids , vol.13 , pp. 739-757
    • MacKinnon, R.J.1    Johnson, R.W.2
  • 9
    • 0030171562 scopus 로고    scopus 로고
    • Essentially compact schemes for unsteady viscous incompressible flows
    • E W., Liu J.-G. Essentially compact schemes for unsteady viscous incompressible flows. J. Comput. Phys. 1996, 128:122-138.
    • (1996) J. Comput. Phys. , vol.128 , pp. 122-138
    • E, W.1    Liu, J.-G.2
  • 10
    • 0030584561 scopus 로고    scopus 로고
    • Vorticity boundary condition and related issues for finite difference schemes
    • E W., Liu J.-G. Vorticity boundary condition and related issues for finite difference schemes. J. Comput. Phys. 1996, 124:368-382.
    • (1996) J. Comput. Phys. , vol.124 , pp. 368-382
    • E, W.1    Liu, J.-G.2
  • 11
    • 0000213656 scopus 로고    scopus 로고
    • Projection method I: convergence and numerical boundary layers
    • E W., Liu J.-G. Projection method I: convergence and numerical boundary layers. SIAM J. Numer. Anal. 1996, 33:1017-1057.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1017-1057
    • E, W.1    Liu, J.-G.2
  • 12
    • 0001144269 scopus 로고    scopus 로고
    • Projection method. II: Godunov-Ryabenki analysis
    • E W., Liu J.-G. Projection method. II: Godunov-Ryabenki analysis. SIAM J. Numer. Anal. 1996, 33:1597-1621.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1597-1621
    • E, W.1    Liu, J.-G.2
  • 13
    • 40449093496 scopus 로고
    • A numerical method for solving incompressible viscous flow problems
    • Chorin A.J. A numerical method for solving incompressible viscous flow problems. J. Comput. Phys. 1967, 2:12-26.
    • (1967) J. Comput. Phys. , vol.2 , pp. 12-26
    • Chorin, A.J.1
  • 14
    • 0026137540 scopus 로고
    • Steady and unsteady solutions of the incompressible Navier-Stokes equations
    • Rogers S., Kuak D., Kiris C. Steady and unsteady solutions of the incompressible Navier-Stokes equations. AIAA J. 1991, 29(4):603-610.
    • (1991) AIAA J. , vol.29 , Issue.4 , pp. 603-610
    • Rogers, S.1    Kuak, D.2    Kiris, C.3
  • 15
    • 0003981573 scopus 로고    scopus 로고
    • Higher-order compact schemes for numerical simulation of incompressible flows
    • ICASE Report 98-13, ICASE, Langley Research Center,
    • R.V. Wilson, A.O. Demuren, M.H. Carpenter, Higher-order compact schemes for numerical simulation of incompressible flows, ICASE Report 98-13, ICASE, Langley Research Center, 1998.
    • (1998)
    • Wilson, R.V.1    Demuren, A.O.2    Carpenter, M.H.3
  • 16
    • 84968483581 scopus 로고
    • On the convergence of discrete approximations of the Navier-Stokes equations
    • Chorin A.J. On the convergence of discrete approximations of the Navier-Stokes equations. Math. Comput. 1969, 23:341-353.
    • (1969) Math. Comput. , vol.23 , pp. 341-353
    • Chorin, A.J.1
  • 17
    • 0001608079 scopus 로고
    • A second-order projection method for the incompressible Navier-Stokes equations
    • Bell J.B., Colella P., Glaz H.M. A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys. 1989, 85:257-283.
    • (1989) J. Comput. Phys. , vol.85 , pp. 257-283
    • Bell, J.B.1    Colella, P.2    Glaz, H.M.3
  • 18
    • 0033566235 scopus 로고    scopus 로고
    • Numerical solution of the incompressible Navier-Stokes equations with an upwind compact difference scheme
    • Ma Y., Fu D., Kobarash T., Taniguchi N. Numerical solution of the incompressible Navier-Stokes equations with an upwind compact difference scheme. Int. J. Numer. Methods Fluids 1999, 30:509-521.
    • (1999) Int. J. Numer. Methods Fluids , vol.30 , pp. 509-521
    • Ma, Y.1    Fu, D.2    Kobarash, T.3    Taniguchi, N.4
  • 19
    • 33044504607 scopus 로고
    • A calculation procedure for heat, mass and momentum transfer in three dimensional parabolic flows
    • Patanker S.V., Spalding D.B. A calculation procedure for heat, mass and momentum transfer in three dimensional parabolic flows. Int. J. Heat Mass Trans. 1972, 15:1787-1806.
    • (1972) Int. J. Heat Mass Trans. , vol.15 , pp. 1787-1806
    • Patanker, S.V.1    Spalding, D.B.2
  • 20
    • 0029380108 scopus 로고
    • High-order compact scheme for the steady stream-function vorticity equations
    • Spotz W.F., Carey G.F. High-order compact scheme for the steady stream-function vorticity equations. Int. J. Numer. Methods Eng. 1995, 38:3497-3512.
    • (1995) Int. J. Numer. Methods Eng. , vol.38 , pp. 3497-3512
    • Spotz, W.F.1    Carey, G.F.2
  • 21
    • 33845639198 scopus 로고    scopus 로고
    • High-order compact exponential finite difference methods for convection-diffusion type problems
    • Tian Z.F., Dai S.Q. High-order compact exponential finite difference methods for convection-diffusion type problems. J. Comput. Phys. 2007, 220:952-974.
    • (2007) J. Comput. Phys. , vol.220 , pp. 952-974
    • Tian, Z.F.1    Dai, S.Q.2
  • 22
    • 0037456263 scopus 로고    scopus 로고
    • A fourth-order compact finite difference scheme for the steady streamfunction-vorticity formulation of the Navier-Stokes/Boussinesq equations
    • Tian Z.F., Ge Y.B. A fourth-order compact finite difference scheme for the steady streamfunction-vorticity formulation of the Navier-Stokes/Boussinesq equations. Int. J. Numer. Methods Fluids. 2003, 41:495-518.
    • (2003) Int. J. Numer. Methods Fluids. , vol.41 , pp. 495-518
    • Tian, Z.F.1    Ge, Y.B.2
  • 24
    • 0003134208 scopus 로고
    • Hybrid biconjugate methods for CFD problems
    • M. Hafez, K. Oshima (Eds.), Computational Fluid Dynamics Review,
    • G.L.G. Sleijpen, H.A. van der Vorst, Hybrid biconjugate methods for CFD problems, M. Hafez, K. Oshima (Eds.), Computational Fluid Dynamics Review, 1995, pp. 457-476.
    • (1995) , pp. 457-476
    • Sleijpen, G.L.G.1    van der Vorst, H.A.2
  • 25
    • 0003872107 scopus 로고
    • High-Order Compact Finite Difference Schemes for Computational Mechanics
    • Ph.D. Thesis, University of Texas at Austin, Austin, TX,
    • W.F. Spotz, High-Order Compact Finite Difference Schemes for Computational Mechanics, Ph.D. Thesis, University of Texas at Austin, Austin, TX, 1995.
    • (1995)
    • Spotz, W.F.1
  • 26
    • 0004574861 scopus 로고
    • Simulation of cavity flows by the lattice Boltzmann method
    • Hou S., Zou Q., Chen S., Doolen G., Cogley A. Simulation of cavity flows by the lattice Boltzmann method. J. Comput. Phys. 1995, 118:329-347.
    • (1995) J. Comput. Phys. , vol.118 , pp. 329-347
    • Hou, S.1    Zou, Q.2    Chen, S.3    Doolen, G.4    Cogley, A.5
  • 27
    • 18344385504 scopus 로고    scopus 로고
    • A new paradigm for solving Navier-Stokes equations: streamfunction-velocity formulation
    • Gupta M.M., Kalita J.C. A new paradigm for solving Navier-Stokes equations: streamfunction-velocity formulation. J. Comput. Phys. 2005, 207:52-68.
    • (2005) J. Comput. Phys. , vol.207 , pp. 52-68
    • Gupta, M.M.1    Kalita, J.C.2
  • 28
    • 17144404238 scopus 로고    scopus 로고
    • A pure-compact scheme for the streamfunction formulation of Navier-Stokes equations
    • Ben-Artzi M., Croisille J.-P., Fishelov D., Trachtenberg S. A pure-compact scheme for the streamfunction formulation of Navier-Stokes equations. J. Comput. Phys. 2005, 205:640-664.
    • (2005) J. Comput. Phys. , vol.205 , pp. 640-664
    • Ben-Artzi, M.1    Croisille, J.-P.2    Fishelov, D.3    Trachtenberg, S.4
  • 29
    • 0036202978 scopus 로고    scopus 로고
    • A central-difference scheme for a pure stream function formulation of incompressible viscous flows
    • Kupferman R. A central-difference scheme for a pure stream function formulation of incompressible viscous flows. SIAM J. Sci. Comput. 2001, 23:1-18.
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 1-18
    • Kupferman, R.1
  • 30
    • 0037196857 scopus 로고    scopus 로고
    • A stream function implicit finite deifference scheme for 2D incompressible flows of Newtonian fluids
    • Bubnovich V.I., Rosas C.E., Moraga N.O. A stream function implicit finite deifference scheme for 2D incompressible flows of Newtonian fluids. Int. J. Numer. Methods Eng. 2002, 53:2163-2184.
    • (2002) Int. J. Numer. Methods Eng. , vol.53 , pp. 2163-2184
    • Bubnovich, V.I.1    Rosas, C.E.2    Moraga, N.O.3
  • 31
    • 15844377785 scopus 로고    scopus 로고
    • A computational stream function method for two-dimensioanl incompressible viscous flows
    • Kobayashi M.H., Pereira J.M.C. A computational stream function method for two-dimensioanl incompressible viscous flows. Int. J. Numer. Methods Eng. 2005, 62:1950-1981.
    • (2005) Int. J. Numer. Methods Eng. , vol.62 , pp. 1950-1981
    • Kobayashi, M.H.1    Pereira, J.M.C.2
  • 32
    • 0035505399 scopus 로고    scopus 로고
    • An efficient high-order Taylor weak statement formulation for the Navier-Stokes equations
    • Kolesnikov A., Baker A.J. An efficient high-order Taylor weak statement formulation for the Navier-Stokes equations. J. Comput. Phys. 2001, 173:549-574.
    • (2001) J. Comput. Phys. , vol.173 , pp. 549-574
    • Kolesnikov, A.1    Baker, A.J.2
  • 33
    • 13944273013 scopus 로고    scopus 로고
    • Multigrid method for the streamfunction formulation of the 2D incompressible Navier-Stokes equations
    • (in Chinese)
    • Tian R.X., Ge Y.B., Wu W.Q. Multigrid method for the streamfunction formulation of the 2D incompressible Navier-Stokes equations. J. Eng. Thermophys. 2005, 26:31-34. (in Chinese).
    • (2005) J. Eng. Thermophys. , vol.26 , pp. 31-34
    • Tian, R.X.1    Ge, Y.B.2    Wu, W.Q.3
  • 34
    • 0000005482 scopus 로고
    • BiCGSTAB: a fast and smoothly converging variant of BiCG for the solution of nonsymmetric linear systems
    • van Der Vorst H. BiCGSTAB: a fast and smoothly converging variant of BiCG for the solution of nonsymmetric linear systems. SIAM J. Sci. Comput. 1992, 13:631-644.
    • (1992) SIAM J. Sci. Comput. , vol.13 , pp. 631-644
    • van Der Vorst, H.1
  • 36
    • 0003430379 scopus 로고    scopus 로고
    • Multigrid acceleration techniques and applications to the numerical solution of partial differential equation
    • Ph.D. Thesis, George Washington Univ.,
    • J. Zhang, Multigrid acceleration techniques and applications to the numerical solution of partial differential equation, Ph.D. Thesis, George Washington Univ., 1997.
    • (1997)
    • Zhang, J.1
  • 37
    • 85041130800 scopus 로고    scopus 로고
    • Numerical simulation of 2D square driven cavity using fourth-order compact finite difference schemes
    • Zhang J. Numerical simulation of 2D square driven cavity using fourth-order compact finite difference schemes. Comput. Math. Appl. 2003, 45:43-52.
    • (2003) Comput. Math. Appl. , vol.45 , pp. 43-52
    • Zhang, J.1
  • 38
    • 46149132843 scopus 로고
    • Block-implicit multigrid solution of Navier-Stokes equations in primitive variables
    • Vanka S.P. Block-implicit multigrid solution of Navier-Stokes equations in primitive variables. J. Comput. Phys. 1986, 65:138-158.
    • (1986) J. Comput. Phys. , vol.65 , pp. 138-158
    • Vanka, S.P.1
  • 39
    • 0031171880 scopus 로고    scopus 로고
    • Streamfunction-vorticity driven cavity solution using p finite elements
    • Barragy E., Carey G.F. Streamfunction-vorticity driven cavity solution using p finite elements. Comput. Fluid 1997, 26:453-468.
    • (1997) Comput. Fluid , vol.26 , pp. 453-468
    • Barragy, E.1    Carey, G.F.2
  • 40
    • 0032078546 scopus 로고    scopus 로고
    • Benchmark spectral results on the lid-driven cavity flow
    • Botella O., Peyret R. Benchmark spectral results on the lid-driven cavity flow. Comput. Fluid 1998, 27:421-433.
    • (1998) Comput. Fluid , vol.27 , pp. 421-433
    • Botella, O.1    Peyret, R.2
  • 41
    • 0000305272 scopus 로고
    • An efficient scheme for solving steady incompressible Navier-Stokes equations
    • Bruneau C.-H., Jouron C. An efficient scheme for solving steady incompressible Navier-Stokes equations. J. Comput. Phys. 1990, 89:389-413.
    • (1990) J. Comput. Phys. , vol.89 , pp. 389-413
    • Bruneau, C.-H.1    Jouron, C.2
  • 42
    • 85190572662 scopus 로고
    • Numerical simulation of instability in driven rectangular cavity flos
    • (in Chinese)
    • Wu Y., Fu D., Huang L. Numerical simulation of instability in driven rectangular cavity flos. Acta Mech. Sin. 1994, 26(4):397-406. (in Chinese).
    • (1994) Acta Mech. Sin. , vol.26 , Issue.4 , pp. 397-406
    • Wu, Y.1    Fu, D.2    Huang, L.3
  • 43
    • 0026833160 scopus 로고
    • Higher-order solutions of square driven cavity flow using a variable-order multigrid method
    • Nishida H., Satofuka N. Higher-order solutions of square driven cavity flow using a variable-order multigrid method. Int. J. Numer. Methods Eng. 1992, 34:637-653.
    • (1992) Int. J. Numer. Methods Eng. , vol.34 , pp. 637-653
    • Nishida, H.1    Satofuka, N.2
  • 44
    • 0037986168 scopus 로고    scopus 로고
    • A novel fully-implicit finite volume method applied to the lid-driven cavity problem. Part I: High Reynolds number flow calculations
    • Sahin M., Owens R.G. A novel fully-implicit finite volume method applied to the lid-driven cavity problem. Part I: High Reynolds number flow calculations. Int. J. Numer. Methods Fluids 2003, 42:57-77.
    • (2003) Int. J. Numer. Methods Fluids , vol.42 , pp. 57-77
    • Sahin, M.1    Owens, R.G.2
  • 45
    • 0035629242 scopus 로고    scopus 로고
    • Vorticity dynamics and numerical resolution of Navier-Stokes equations
    • Ben-Artzi M., Fishelov D., Trachtenberg S. Vorticity dynamics and numerical resolution of Navier-Stokes equations. Math. Model. Numer. Anal. 2001, 35(2):313-330.
    • (2001) Math. Model. Numer. Anal. , vol.35 , Issue.2 , pp. 313-330
    • Ben-Artzi, M.1    Fishelov, D.2    Trachtenberg, S.3
  • 46
    • 21144452940 scopus 로고    scopus 로고
    • A compact scheme for the stream-function formulation of Navier-Stokes equations
    • Springer-Verlag., 2667
    • Fishelov D., Ben-Artzi M., Croisille J.-P. A compact scheme for the stream-function formulation of Navier-Stokes equations. Notes on Computer Science 2003, vol. 2667. Springer-Verlag.
    • (2003) Notes on Computer Science
    • Fishelov, D.1    Ben-Artzi, M.2    Croisille, J.-P.3
  • 47
    • 33845650175 scopus 로고    scopus 로고
    • Convergence of a compact scheme for the pure streamfunction formulation of the unsteady Navier-Stokes system
    • Ben-Artzi M., Croisille J.-P., Fishelov D. Convergence of a compact scheme for the pure streamfunction formulation of the unsteady Navier-Stokes system. SIAM J. Numer. Anal. 2006, 44(5):1997-2024.
    • (2006) SIAM J. Numer. Anal. , vol.44 , Issue.5 , pp. 1997-2024
    • Ben-Artzi, M.1    Croisille, J.-P.2    Fishelov, D.3
  • 48
    • 77951116123 scopus 로고    scopus 로고
    • A compact difference scheme for the biharmonic equation in planar irregular domains
    • Ben-Artzi M., Chorev I., Croisille J.-P., Fishelov D. A compact difference scheme for the biharmonic equation in planar irregular domains. SIAM J. Numer. Anal. 2009, 47:3087-3108.
    • (2009) SIAM J. Numer. Anal. , vol.47 , pp. 3087-3108
    • Ben-Artzi, M.1    Chorev, I.2    Croisille, J.-P.3    Fishelov, D.4
  • 49
    • 49749100474 scopus 로고    scopus 로고
    • On the use of compact streamfunction-velocity formulation of steady Navier-Stokes equations on geometries beyond rectangular
    • Pandit S.K. On the use of compact streamfunction-velocity formulation of steady Navier-Stokes equations on geometries beyond rectangular. J. Sci. Comput. 2008, 36:219-242.
    • (2008) J. Sci. Comput. , vol.36 , pp. 219-242
    • Pandit, S.K.1
  • 50
    • 0345761443 scopus 로고    scopus 로고
    • A transformation-free HOC scheme for steady-state convection-diffusion on non-uniform grids
    • Kalita J.C., Dass A.K., Dalal D.C. A transformation-free HOC scheme for steady-state convection-diffusion on non-uniform grids. Int. J. Numer. Methods Fluids 2004, 44:33-53.
    • (2004) Int. J. Numer. Methods Fluids , vol.44 , pp. 33-53
    • Kalita, J.C.1    Dass, A.K.2    Dalal, D.C.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.