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Volumn 198, Issue 1, 2007, Pages 268-286

A fourth-order compact ADI method for solving two-dimensional unsteady convection-diffusion problems

Author keywords

Alternating direction implicit method; Convection diffusion; Higher order compact scheme; Unsteady

Indexed keywords

DIFFERENCE EQUATIONS; FINITE DIFFERENCE METHOD; FOURIER TRANSFORMS; MATRIX ALGEBRA; NUMERICAL METHODS; PROBLEM SOLVING;

EID: 33748413373     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.12.005     Document Type: Article
Times cited : (100)

References (31)
  • 2
    • 0001458266 scopus 로고
    • 4 exponential finite difference scheme for convection diffusion equation
    • 4 exponential finite difference scheme for convection diffusion equation. J. Comput. Phys. 104 (1993) 129-139
    • (1993) J. Comput. Phys. , vol.104 , pp. 129-139
    • Chen, G.Q.1    Gao, Z.2    Yang, Z.F.3
  • 3
    • 0008466688 scopus 로고
    • The operator compact implicit method for parabolic equations
    • Ciment M., Leventhal S.H., and Weinberg B.C. The operator compact implicit method for parabolic equations. J. Comput. Phys. 28 (1978) 135-166
    • (1978) J. Comput. Phys. , vol.28 , pp. 135-166
    • Ciment, M.1    Leventhal, S.H.2    Weinberg, B.C.3
  • 4
    • 0036495593 scopus 로고    scopus 로고
    • Compact ADI method for solving parabolic differential equations
    • Dai W., and Nassar R. Compact ADI method for solving parabolic differential equations. Numer. Meth. Partial Differential Eq. 18 (2002) 129-142
    • (2002) Numer. Meth. Partial Differential Eq. , vol.18 , pp. 129-142
    • Dai, W.1    Nassar, R.2
  • 5
    • 0001533213 scopus 로고
    • Relaxation methods applied to determine the motion in two dimensions of a viscous fluid past a fixed cylinder
    • de G Allen D.N., and Southwell R.V. Relaxation methods applied to determine the motion in two dimensions of a viscous fluid past a fixed cylinder. Quart. J. Mech. Appl. Math. 8 (1955) 129-143
    • (1955) Quart. J. Mech. Appl. Math. , vol.8 , pp. 129-143
    • de G Allen, D.N.1    Southwell, R.V.2
  • 6
    • 0000324432 scopus 로고
    • Finite difference associated with second-order difference equations
    • Dennis S.C.R. Finite difference associated with second-order difference equations. Quart. J. Mech. Appl. Math. 13 (1960) 487-507
    • (1960) Quart. J. Mech. Appl. Math. , vol.13 , pp. 487-507
    • Dennis, S.C.R.1
  • 7
    • 0003807856 scopus 로고
    • Accurate representations of partial differential equations by finite difference schemes
    • Dennis S.C.R., and Hudson J.D. Accurate representations of partial differential equations by finite difference schemes. J. Inst. Math. Appl. 23 (1979) 43-51
    • (1979) J. Inst. Math. Appl. , vol.23 , pp. 43-51
    • Dennis, S.C.R.1    Hudson, J.D.2
  • 8
    • 0000468321 scopus 로고
    • 4 finite-difference approximations to operators of Navier-Stokes type
    • 4 finite-difference approximations to operators of Navier-Stokes type. J. Comput. Phys. 85 (1989) 390-416
    • (1989) J. Comput. Phys. , vol.85 , pp. 390-416
    • Dennis, S.C.R.1    Hudson, J.D.2
  • 10
    • 0021207821 scopus 로고
    • A single cell high order scheme for the convection-diffusion equation with variable coefficients
    • Gupta M.M., Manohar R.P., and Stephenson J.W. A single cell high order scheme for the convection-diffusion equation with variable coefficients. Int. J. Numer. Meth. Fluids 4 (1984) 641-651
    • (1984) Int. J. Numer. Meth. Fluids , vol.4 , pp. 641-651
    • Gupta, M.M.1    Manohar, R.P.2    Stephenson, J.W.3
  • 11
    • 0003102291 scopus 로고
    • Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique
    • Hirsh R.S. Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique. J. Comput. Phys. 19 (1975) 90-109
    • (1975) J. Comput. Phys. , vol.19 , pp. 90-109
    • Hirsh, R.S.1
  • 12
    • 0037197866 scopus 로고    scopus 로고
    • A class of higher order compact schemes for the unsteady two-dimensional convection-diffusion equation with variable convection coefficients
    • Kalita J.C., Dalal D.C., and Dass A.K. A class of higher order compact schemes for the unsteady two-dimensional convection-diffusion equation with variable convection coefficients. Int. J. Numer. Meth. Fluids 38 (2002) 1111-1131
    • (2002) Int. J. Numer. Meth. Fluids , vol.38 , pp. 1111-1131
    • Kalita, J.C.1    Dalal, D.C.2    Dass, A.K.3
  • 13
    • 3042771625 scopus 로고    scopus 로고
    • High order ADI method for solving unsteady convection-diffusion problems
    • Karaa S., and Zhang J. High order ADI method for solving unsteady convection-diffusion problems. J. Comput. Phys. 198 (2004) 1-9
    • (2004) J. Comput. Phys. , vol.198 , pp. 1-9
    • Karaa, S.1    Zhang, J.2
  • 14
    • 0029106259 scopus 로고
    • A compact fourth-order finite difference scheme for the incompressible Navier-Stokes equations
    • Li M., Tang T., and Fornberg B. A compact fourth-order finite difference scheme for the incompressible Navier-Stokes equations. Int. J. Numer. Meth. Fluids 20 (1995) 1137-1151
    • (1995) Int. J. Numer. Meth. Fluids , vol.20 , pp. 1137-1151
    • Li, M.1    Tang, T.2    Fornberg, B.3
  • 16
    • 0024050730 scopus 로고
    • A third-order semi-implicit finite difference method for solving the one-dimensional convection-diffusion equation
    • Noye B.J., and Tan H.H. A third-order semi-implicit finite difference method for solving the one-dimensional convection-diffusion equation. Int. J. Numer. Meth. Eng. 26 (1988) 1615-1629
    • (1988) Int. J. Numer. Meth. Eng. , vol.26 , pp. 1615-1629
    • Noye, B.J.1    Tan, H.H.2
  • 17
    • 0024304690 scopus 로고
    • Finite difference methods for solving the two-dimensional advection-diffusion equation
    • Noye B.J., and Tan H.H. Finite difference methods for solving the two-dimensional advection-diffusion equation. Int. J. Numer. Meth. Fluids 9 (1989) 75-89
    • (1989) Int. J. Numer. Meth. Fluids , vol.9 , pp. 75-89
    • Noye, B.J.1    Tan, H.H.2
  • 19
    • 0002058827 scopus 로고
    • The numerical solution of parabolic and elliptic differential equations
    • Peaceman D.W., and Rachford Jr. H.H. The numerical solution of parabolic and elliptic differential equations. J. Soc. Ind. Appl. Math. 3 (1959) 28-41
    • (1959) J. Soc. Ind. Appl. Math. , vol.3 , pp. 28-41
    • Peaceman, D.W.1    Rachford Jr., H.H.2
  • 20
    • 0007747818 scopus 로고
    • High order difference schemes for unsteady one-dimensional convection-diffusion problems
    • Rigal A. High order difference schemes for unsteady one-dimensional convection-diffusion problems. J. Comput. Phys. 114 (1994) 59-76
    • (1994) J. Comput. Phys. , vol.114 , pp. 59-76
    • Rigal, A.1
  • 22
    • 0001510378 scopus 로고
    • New methods for the derivation of stable difference representations for differential equations
    • Roscoe D.F. New methods for the derivation of stable difference representations for differential equations. J. Inst. Math. Appl. 16 (1975) 291-301
    • (1975) J. Inst. Math. Appl. , vol.16 , pp. 291-301
    • Roscoe, D.F.1
  • 23
    • 0001688935 scopus 로고
    • Aspects of numerical methods for elliptic singular perturbation problems
    • Segal A. Aspects of numerical methods for elliptic singular perturbation problems. SIAM J. Sci. Statist. Comput. 3 (1982) 327-349
    • (1982) SIAM J. Sci. Statist. Comput. , vol.3 , pp. 327-349
    • Segal, A.1
  • 24
    • 0015368687 scopus 로고
    • A novel finite difference formulation for differential equations involving both first and second derivatives
    • Spalding D.B. A novel finite difference formulation for differential equations involving both first and second derivatives. Int. J. Numer. Meth. Eng. 4 (1972) 551-559
    • (1972) Int. J. Numer. Meth. Eng. , vol.4 , pp. 551-559
    • Spalding, D.B.1
  • 25
    • 0029380108 scopus 로고
    • High-order compact scheme for the steady stream-function vorticity equations
    • Spotz W.F., and Carey G.F. High-order compact scheme for the steady stream-function vorticity equations. Int. J. Numer. Meth. Eng. 38 (1995) 3497-3512
    • (1995) Int. J. Numer. Meth. Eng. , vol.38 , pp. 3497-3512
    • Spotz, W.F.1    Carey, G.F.2
  • 26
    • 0035499484 scopus 로고    scopus 로고
    • Extension of high-order compact schemes to time-dependent problems
    • Spotz W.F., and Carey G.F. Extension of high-order compact schemes to time-dependent problems. Numer. Meth. Partial Differential Eq. 17 (2001) 657-672
    • (2001) Numer. Meth. Partial Differential Eq. , vol.17 , pp. 657-672
    • Spotz, W.F.1    Carey, G.F.2
  • 28
    • 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., and 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. Meth. Fluids 41 (2003) 495-518
    • (2003) Int. J. Numer. Meth. Fluids , vol.41 , pp. 495-518
    • Tian, Z.F.1    Ge, Y.B.2
  • 29
    • 0032030123 scopus 로고    scopus 로고
    • An explicit fourth-order compact finite difference scheme for three dimensional convection-diffusion equation
    • Zhang J. An explicit fourth-order compact finite difference scheme for three dimensional convection-diffusion equation. Commun. Numer. Meth. Eng. 14 (1998) 209-218
    • (1998) Commun. Numer. Meth. Eng. , vol.14 , pp. 209-218
    • Zhang, J.1
  • 30
    • 85041102747 scopus 로고    scopus 로고
    • Preconditioned iterative methods and finite difference schemes for convection-diffusion
    • Zhang J. Preconditioned iterative methods and finite difference schemes for convection-diffusion. Appl. Math. Comput. 109 (2000) 11-30
    • (2000) Appl. Math. Comput. , vol.109 , pp. 11-30
    • Zhang, J.1
  • 31
    • 0037054321 scopus 로고    scopus 로고
    • Multigrid method and fourth order compact difference scheme for 2D Poisson equation unequal meshsize discretization
    • Zhang J. Multigrid method and fourth order compact difference scheme for 2D Poisson equation unequal meshsize discretization. J. Comput. Phys. 179 (2002) 170-179
    • (2002) J. Comput. Phys. , vol.179 , pp. 170-179
    • Zhang, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.