메뉴 건너뛰기




Volumn 22, Issue 4, 2006, Pages 983-993

A high-order compact ADI method for solving three-dimensional unsteady convection-diffusion problems

Author keywords

ADI method; High order compact scheme; Stability; Unsteady convection diffusion problem

Indexed keywords


EID: 33745799513     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20134     Document Type: Article
Times cited : (44)

References (29)
  • 1
    • 0003537973 scopus 로고
    • Computational fluid dynamics
    • 1 P. J. Roach, Computational fluid dynamics, Hermosa, Albuquerque, NM, 1976.
    • (1976)
    • Roach, P.J.1
  • 2
    • 17644370618 scopus 로고
    • Heat transfer to a draining film
    • 2 J. Iserberg, C. Gutfinger, Heat transfer to a draining film, Int Heat Transfer 16 ( 1972), 505–512.
    • (1972) Int Heat Transfer , vol.16 , pp. 505-512
    • Iserberg, J.1    Gutfinger, C.2
  • 3
    • 0018926889 scopus 로고
    • Water transport in soils
    • 3 J. Y. Parlarge, Water transport in soils, Anna Rev Fluid Mech 2 ( 1980), 77–102.
    • (1980) Anna Rev Fluid Mech , vol.2 , pp. 77-102
    • Parlarge, J.Y.1
  • 4
    • 0020971618 scopus 로고
    • Numerical solutions of solute transport in inconfined aquifers
    • 4 V. Guvanasen, R. E. Volker, Numerical solutions of solute transport in inconfined aquifers, Int J Numer Methods Fluids 3 ( 1983), 103–123.
    • (1983) Int J Numer Methods Fluids , vol.3 , pp. 103-123
    • Guvanasen, V.1    Volker, R.E.2
  • 5
    • 0021822768 scopus 로고
    • Dispersion in anisotropic homogeneous porous media
    • 5 Q. N. Fattah, J. A. Hoopes, Dispersion in anisotropic homogeneous porous media, J Hydraul Eng 111 ( 1985), 810–827.
    • (1985) J Hydraul Eng , vol.111 , pp. 810-827
    • Fattah, Q.N.1    Hoopes, J.A.2
  • 6
    • 0020971974 scopus 로고
    • Unsteady flow against dispersion in finite porous media
    • 6 N. Kumar, Unsteady flow against dispersion in finite porous media, J Hydrol 63 ( 1988), 345–385.
    • (1988) J Hydrol , vol.63 , pp. 345-385
    • Kumar, N.1
  • 7
    • 0021784814 scopus 로고
    • Mathematical models of dispersion in rivers and estuaries
    • 7 P. C. Chatwin, C. M. Allen, Mathematical models of dispersion in rivers and estuaries, Anna Rev Fluid Mech 17 ( 1985), 119–149.
    • (1985) Anna Rev Fluid Mech , vol.17 , pp. 119-149
    • Chatwin, P.C.1    Allen, C.M.2
  • 8
    • 0020550785 scopus 로고
    • Modelling of unsteady‐flow water temperatures
    • 8 M. H. Chaudhry, D. E. Class, J. E. Edinger, Modelling of unsteady‐flow water temperatures, J Hydraul Eng 109 ( 1983), 657–669.
    • (1983) J Hydraul Eng , vol.109 , pp. 657-669
    • Chaudhry, M.H.1    Class, D.E.2    Edinger, J.E.3
  • 9
    • 0142009303 scopus 로고
    • Implementation of a variable stepsize variable formula method in the time‐integration part of a code for treatment of long‐range transport of air pollutants
    • 9 Z. Zlatev, R. Berkowicz, L. P. Prahm, Implementation of a variable stepsize variable formula method in the time‐integration part of a code for treatment of long‐range transport of air pollutants, J Comput Phys 55 (2) ( 1984), 278–301.
    • (1984) J Comput Phys , vol.55 , Issue.2 , pp. 278-301
    • Zlatev, Z.1    Berkowicz, R.2    Prahm, L.P.3
  • 10
    • 0024050730 scopus 로고
    • A third‐order semi‐implicit finite difference method for solving the one‐dimensional convection‐diffusion equation
    • 10 B. J. Noye, H. H. Tan, A third‐order semi‐implicit finite difference method for solving the one‐dimensional convection‐diffusion equation, Int J Numer Methods Engrg 26 ( 1988), 1615–1629.
    • (1988) Int J Numer Methods Engrg , vol.26 , pp. 1615-1629
    • Noye, B.J.1    Tan, H.H.2
  • 11
    • 0024050730 scopus 로고
    • Finite difference methods for solving the two‐dimensional advection‐diffusion equation
    • 11 B. J. Noye, H. H. Tan, Finite difference methods for solving the two‐dimensional advection‐diffusion equation, Int J Numer Methods Fluids 26 ( 1988), 1615–1629.
    • (1988) Int J Numer Methods Fluids , vol.26 , pp. 1615-1629
    • Noye, B.J.1    Tan, H.H.2
  • 12
    • 0007747818 scopus 로고
    • High‐order difference schemes for unsteady one‐dimensional diffusion‐convection problems
    • 12 A. Rigal, High‐order difference schemes for unsteady one‐dimensional diffusion‐convection problems, J Comput Phys 114 ( 1994), 59–76.
    • (1994) J Comput Phys , vol.114 , pp. 59-76
    • Rigal, A.1
  • 13
    • 3042758465 scopus 로고    scopus 로고
    • Schémas compacts d'ordre élevé: application aux problémes bidimensionnels de diffusion‐convection instationnaire I
    • 13 A. Rigal, Schémas compacts d'ordre élevé: application aux problémes bidimensionnels de diffusion‐convection instationnaire I, CR Acad Sci Paris Sr I Math 328 ( 1999), 535–538.
    • (1999) CR Acad Sci Paris Sr I Math , vol.328 , pp. 535-538
    • Rigal, A.1
  • 14
    • 0021207821 scopus 로고
    • A single cell high‐order scheme for the convection‐diffusion equation with variable coefficients
    • 14 M. M. Gupta, R. P. Manohar, J. W. Stephenson, A single cell high‐order scheme for the convection‐diffusion equation with variable coefficients, Int J Numer Methods Fluids 4 ( 1984), 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
  • 15
    • 0035499484 scopus 로고    scopus 로고
    • Extension of high‐order compact schemes to time‐dependent problems
    • 15 W. F. Spotz, G. F. Carey, Extension of high‐order compact schemes to time‐dependent problems, Numer Methods Partial Differential Eq 17 ( 2001), 657–672.
    • (2001) Numer Methods Partial Differential Eq , vol.17 , pp. 657-672
    • Spotz, W.F.1    Carey, G.F.2
  • 16
    • 0037197866 scopus 로고    scopus 로고
    • A class of higher order compact schemes for the unsteady two‐dimensional convection‐diffusion equation with variable convection coefficients
    • 16 J. C. Kalita, D. C. Dalal, A. K. Dass, A class of higher order compact schemes for the unsteady two‐dimensional convection‐diffusion equation with variable convection coefficients, Int J Numer Methods Fluids 38 ( 2002), 1111–1131.
    • (2002) Int J Numer Methods Fluids , vol.38 , pp. 1111-1131
    • Kalita, J.C.1    Dalal, D.C.2    Dass, A.K.3
  • 17
    • 85120588514 scopus 로고    scopus 로고
    • A class of two‐level compact implicit implicit schemes for solving three‐dimensional unsteady convection‐diffusion problems
    • 17 S. Karaa, A class of two‐level compact implicit implicit schemes for solving three‐dimensional unsteady convection‐diffusion problems, submitted for publication.
    • Karaa, S.1
  • 18
    • 0003095767 scopus 로고
    • Improved forms of the alternating direction methods of Douglas, Peaceman, and Rachford for solving parabolicand elliptic equations
    • 18 A. R. Mitchell, G. Fairweather, Improved forms of the alternating direction methods of Douglas, Peaceman, and Rachford for solving parabolicand elliptic equations, Numer Math 6 ( 1964), 285–292.
    • (1964) Numer Math , vol.6 , pp. 285-292
    • Mitchell, A.R.1    Fairweather, G.2
  • 19
    • 0036495593 scopus 로고    scopus 로고
    • Compact ADI method for solving parabolic differential equations
    • 19 W. Dai, R. Nassar, Compact ADI method for solving parabolic differential equations, Numer Methods Partial Differential Equations 18 (2) ( 2002), 129–142.
    • (2002) Numer Methods Partial Differential Equations , vol.18 , Issue.2 , pp. 129-142
    • Dai, W.1    Nassar, R.2
  • 20
    • 0042850255 scopus 로고
    • High accuracy ADI methods for hyperbolic equations with variable coefficients
    • 20 S. McKee, High accuracy ADI methods for hyperbolic equations with variable coefficients, J Inst Math Appl 11 ( 1973), 105–109.
    • (1973) J Inst Math Appl , vol.11 , pp. 105-109
    • McKee, S.1
  • 21
    • 84949795680 scopus 로고
    • Higher order compact implicit schemes for the wave equation
    • 21 M. Ciment, S. H. Leventhal, Higher order compact implicit schemes for the wave equation, Math Comp 29 ( 1975), 985–994.
    • (1975) Math Comp , vol.29 , pp. 985-994
    • Ciment, M.1    Leventhal, S.H.2
  • 22
    • 3042771625 scopus 로고    scopus 로고
    • High‐order ADI method for solving unsteady convection‐diffusion problems
    • 22 S. Karaa, J. Zhang, High‐order ADI method for solving unsteady convection‐diffusion problems, J Comput Phys 198 (1) ( 2004), 1–9.
    • (2004) J Comput Phys , vol.198 , Issue.1 , pp. 1-9
    • Karaa, S.1    Zhang, J.2
  • 23
    • 0002058827 scopus 로고
    • The numerical solution of parabolic and elliptic differential equations
    • 23 D. W. Peaceman, H. H. Rachford Jr., 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, H.H.2
  • 24
    • 0003872107 scopus 로고
    • High‐order compact finite difference schemes for computational mechanics
    • 24 W. F. Spotz, High‐order compact finite difference schemes for computational mechanics, PhD thesis, University of Texas at Austin, Austin, TX, 1995.
    • (1995)
    • Spotz, W.F.1
  • 25
    • 0032030123 scopus 로고    scopus 로고
    • An explicit fourth‐order compact finite difference scheme for three‐dimensional convection‐diffusion equation
    • 25 J. Zhang, An explicit fourth‐order compact finite difference scheme for three‐dimensional convection‐diffusion equation, Comm Numer Methods Engrg 14 (3) ( 1998), 209–218.
    • (1998) Comm Numer Methods Engrg , vol.14 , Issue.3 , pp. 209-218
    • Zhang, J.1
  • 26
    • 0001742634 scopus 로고
    • A general formulation of alternating direction methods. I. Parabolic and hyperbolic problems
    • 26 J. Douglas Jr., J. E. Gunn, A general formulation of alternating direction methods. I. Parabolic and hyperbolic problems, Numer Math 6 ( 1964), 428–453.
    • (1964) Numer Math , vol.6 , pp. 428-453
    • Douglas, J.1    Gunn, J.E.2
  • 27
    • 0942266745 scopus 로고    scopus 로고
    • Numerical solution of the three‐dimensional advection‐diffusion equation
    • 27 M. Dehghan, Numerical solution of the three‐dimensional advection‐diffusion equation, Appl Math Comput 150 (1) ( 2004), 5–19.
    • (2004) Appl Math Comput , vol.150 , Issue.1 , pp. 5-19
    • Dehghan, M.1
  • 28
    • 0347121979 scopus 로고    scopus 로고
    • Improved accuracy for locally one‐dimensional methods for parabolic equations
    • 28 J. Douglas Jr., S. Kim, Improved accuracy for locally one‐dimensional methods for parabolic equations, Math Models Methods Appl Sci 11 ( 2001), 1563–1579.
    • (2001) Math Models Methods Appl Sci , vol.11 , pp. 1563-1579
    • Douglas, J.1    Kim, S.2
  • 29
    • 0043073181 scopus 로고    scopus 로고
    • Compact schemes for acoustics in the frequency domain
    • 29 S. Kim, Compact schemes for acoustics in the frequency domain, Math Comput Model 37 ( 2003), 1335–1341.
    • (2003) Math Comput Model , vol.37 , pp. 1335-1341
    • Kim, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.