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Volumn 152, Issue 3-4, 1998, Pages 337-359

Numerical analyses of operator-splitting algorithms for the two-dimensional advection-diffusion equation

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; ERROR ANALYSIS; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; INTERPOLATION; MATHEMATICAL OPERATORS;

EID: 0031677005     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(97)00127-8     Document Type: Article
Times cited : (18)

References (44)
  • 1
    • 0017560391 scopus 로고
    • Accurate calculation of transport in two-dimensions
    • F.M. Holly Jr. and A. Preissmann, Accurate calculation of transport in two-dimensions, Proc. ASCE J. Hyd. Div. 103 (1977) 1259-1277.
    • (1977) Proc. ASCE J. Hyd. Div. , vol.103 , pp. 1259-1277
    • Holly F.M., Jr.1    Preissmann, A.2
  • 2
    • 0024656262 scopus 로고
    • An operator splitting algorithm for two-dimensional convection-dispersion-reaction problems
    • D. Ding and P.L.-F. Liu, An operator splitting algorithm for two-dimensional convection-dispersion-reaction problems. Int. J. Numer. Methods Engrg. 28 (1989) 23-40.
    • (1989) Int. J. Numer. Methods Engrg. , vol.28 , pp. 23-40
    • Ding, D.1    Liu, P.L.-F.2
  • 3
    • 0042952505 scopus 로고
    • An explicit Hermitian finite difference scheme for pollutant transport in transient river flows
    • Paris
    • J. Glass and W. Rodi, An explicit Hermitian finite difference scheme for pollutant transport in transient river flows, Proc. 4th GAMM Conf. Numer. Fluid Mech., Paris (1981) 127-136.
    • (1981) Proc. 4th GAMM Conf. Numer. Fluid Mech. , pp. 127-136
    • Glass, J.1    Rodi, W.2
  • 4
    • 0020171389 scopus 로고
    • A higher order numerical scheme for scalar transport
    • J. Glass and W. Rodi, A higher order numerical scheme for scalar transport, Comput. Appl. Mech. Engrg. 31 (1982) 337-358.
    • (1982) Comput. Appl. Mech. Engrg. , vol.31 , pp. 337-358
    • Glass, J.1    Rodi, W.2
  • 6
    • 0024914778 scopus 로고
    • Three-dimensional modeling of pollutant transport
    • M.L. Spaulding, ed., ASCE, New Port, RI
    • A.K.M.Q. Ahsan and M.S. Bruno, Three-dimensional modeling of pollutant transport, in: M.L. Spaulding, ed., Estuarine and Coastal Modeling (ASCE, New Port, RI, 1989) 462-471.
    • (1989) Estuarine and Coastal Modeling , pp. 462-471
    • Ahsan, A.K.M.Q.1    Bruno, M.S.2
  • 7
    • 0026416373 scopus 로고
    • A higher-order Eulerian scheme for coupled advection-diffusion transport
    • G. Yang, P. Belleudy and A. Temperville, A higher-order Eulerian scheme for coupled advection-diffusion transport, Int. J. Numer. Method Fluids 12 (1991) 43-59.
    • (1991) Int. J. Numer. Method Fluids , vol.12 , pp. 43-59
    • Yang, G.1    Belleudy, P.2    Temperville, A.3
  • 8
    • 0020751363 scopus 로고
    • Characteristic method using time-line interpolation
    • D.E. Goldberg and E. Benjamin, Characteristic method using time-line interpolation, Proc. ASCE J. Hyd. Div. 109 (1983) 670-683.
    • (1983) Proc. ASCE J. Hyd. Div. , vol.109 , pp. 670-683
    • Goldberg, D.E.1    Benjamin, E.2
  • 9
    • 0025627549 scopus 로고
    • Time-line interpolation for solution of the dispersion equation
    • J.-C. Yang and E.-L. Hsu, Time-line interpolation for solution of the dispersion equation, J. Hydr. Res. 28 (1990) 503-520.
    • (1990) J. Hydr. Res. , vol.28 , pp. 503-520
    • Yang, J.-C.1    Hsu, E.-L.2
  • 10
    • 0026238716 scopus 로고
    • Investigation of the use of reach-back characteristic method for 2-D dispersion equation
    • J.-C. Yang, K.-N. Chen and H.-Y. Lee, Investigation of the use of reach-back characteristic method for 2-D dispersion equation, Int. J. Numer. Methods Fluids 13 (1991) 841-855.
    • (1991) Int. J. Numer. Methods Fluids , vol.13 , pp. 841-855
    • Yang, J.-C.1    Chen, K.-N.2    Lee, H.-Y.3
  • 12
    • 70350504025 scopus 로고
    • Splitting and alternating direction methods
    • P.G. Ciarlet and J.L. Lions, eds., Elsevier Science Publishers, Amsterdam
    • n (Part 1) (Elsevier Science Publishers, Amsterdam, 1990) 197-462.
    • (1990) n (Part 1) , vol.1 , pp. 197-462
    • Marchuk, G.I.1
  • 14
    • 84966238639 scopus 로고
    • Numerical methods based on additive splitting for hyperbolic partial differential equation
    • R.J. LeVeque and J. Oliger, Numerical methods based on additive splitting for hyperbolic partial differential equation, Math. Comput. 40 (1983) 469-497.
    • (1983) Math. Comput. , vol.40 , pp. 469-497
    • LeVeque, R.J.1    Oliger, J.2
  • 15
    • 0000383020 scopus 로고
    • Some properties and comparative performance of the semi-Lagrangian method of Robert in the solution of the advection-diffusion equation
    • J. Pudykiewicz and A. Staniforth, Some properties and comparative performance of the semi-Lagrangian method of Robert in the solution of the advection-diffusion equation, Atmos.-Ocean 22(3) (1984) 283-308.
    • (1984) Atmos.-Ocean , vol.22 , Issue.3 , pp. 283-308
    • Pudykiewicz, J.1    Staniforth, A.2
  • 16
    • 0021377270 scopus 로고
    • Adaptive Eulerian-Lagrangian finite element for advection-dispersion equation
    • S.P. Neuman, Adaptive Eulerian-Lagrangian finite element for advection-dispersion equation, Int. J. Numer. Methods Engrg. 20 (1984) 321-337.
    • (1984) Int. J. Numer. Methods Engrg. , vol.20 , pp. 321-337
    • Neuman, S.P.1
  • 17
    • 0001235787 scopus 로고
    • Numerical methods for convection dominated problems based on combining the method of characteristics with finite elements or finite difference procedures
    • J. Douglas Jr. and T.F. Russell, Numerical methods for convection dominated problems based on combining the method of characteristics with finite elements or finite difference procedures, SIAM J. Numer. Anal. 19(5) (1982) 871-885.
    • (1982) SIAM J. Numer. Anal. , vol.19 , Issue.5 , pp. 871-885
    • Douglas J., Jr.1    Russell, T.F.2
  • 18
    • 0001518684 scopus 로고
    • On the construction and comparison of difference schemes
    • G. Strang, On the construction and comparison of difference schemes, SIAM J. Numer. Anal. 5 (1968) 506-517.
    • (1968) SIAM J. Numer. Anal. , vol.5 , pp. 506-517
    • Strang, G.1
  • 19
    • 0025684066 scopus 로고
    • A new finite element method for solving compressible Navier-Stokes equations based on an operator splitting method and h-p adaptivity
    • L. Demkowicz, T.J. Oden and W. Rachowicz, A new finite element method for solving compressible Navier-Stokes equations based on an operator splitting method and h-p adaptivity, Comput. Methods Appl. Mech. Engrg. 84 (1990) 275-326.
    • (1990) Comput. Methods Appl. Mech. Engrg. , vol.84 , pp. 275-326
    • Demkowicz, L.1    Oden, T.J.2    Rachowicz, W.3
  • 20
    • 0002615718 scopus 로고
    • An analysis of the fractional step method
    • J.B. Perot, An analysis of the fractional step method, J. Comput. Phys. 108 (1993) 51-58.
    • (1993) J. Comput. Phys. , vol.108 , pp. 51-58
    • Perot, J.B.1
  • 21
    • 0025432553 scopus 로고
    • Least-square characteristics and finite elements for advection-dispersion simulation
    • C.W. Li, Least-square characteristics and finite elements for advection-dispersion simulation, Int. J. Numer. Methods Engrg. 29 (1990) 1343-1358.
    • (1990) Int. J. Numer. Methods Engrg. , vol.29 , pp. 1343-1358
    • Li, C.W.1
  • 22
    • 0026818180 scopus 로고
    • Fractional step solution to slack tide oxygen balance equation
    • C.W. Li, Fractional step solution to slack tide oxygen balance equation, Comm. Appl. Numer. Methods Engrg. 8 (1992) 93-98.
    • (1992) Comm. Appl. Numer. Methods Engrg. , vol.8 , pp. 93-98
    • Li, C.W.1
  • 23
    • 0024471013 scopus 로고
    • An efficient split-operator scheme for 2-D advection-diffusion simulation using finite elements and characteristics
    • Y.S. Li and C.P. Chen, An efficient split-operator scheme for 2-D advection-diffusion simulation using finite elements and characteristics, Appl. Math. Model. 13 (1989) 248-253.
    • (1989) Appl. Math. Model. , vol.13 , pp. 248-253
    • Li, Y.S.1    Chen, C.P.2
  • 26
    • 0027560398 scopus 로고
    • Solution of the advection-diffusion equation using the spline function and finite elements
    • R. Szymkiewicz, Solution of the advection-diffusion equation using the spline function and finite elements, Comm. Appl. Numer. Methods Engrg. 9 (1993) 197-206.
    • (1993) Comm. Appl. Numer. Methods Engrg. , vol.9 , pp. 197-206
    • Szymkiewicz, R.1
  • 27
    • 0024680502 scopus 로고
    • Eulerian-Lagrangian splitting methods for convection dominated equations
    • X.K. Xin and Y.S. Wong, Eulerian-Lagrangian splitting methods for convection dominated equations, Fluid Dyn. Res. 5 (1989) 13-27.
    • (1989) Fluid Dyn. Res. , vol.5 , pp. 13-27
    • Xin, X.K.1    Wong, Y.S.2
  • 28
    • 84966253400 scopus 로고
    • Intermediate boundary conditions for time split methods applied to hyperbolic partial differential equations
    • R.J. LeVeque, Intermediate boundary conditions for time split methods applied to hyperbolic partial differential equations, Math. Comput. 47 (1986) 37-54.
    • (1986) Math. Comput. , vol.47 , pp. 37-54
    • LeVeque, R.J.1
  • 29
    • 0042451520 scopus 로고
    • Intermediate boundary corrections for split operator methods in three dimensions
    • A.R. Gourlay and A.R. Mitchell, Intermediate boundary corrections for split operator methods in three dimensions, BIT 7 (1967) 31-38.
    • (1967) BIT , vol.7 , pp. 31-38
    • Gourlay, A.R.1    Mitchell, A.R.2
  • 30
    • 0019547792 scopus 로고
    • On the treatment of time-dependent boundary conditions in splitting methods for parabolic differential equations
    • B.P. Sommeijer, P.J. van der Houwen and J.W. Verwer, On the treatment of time-dependent boundary conditions in splitting methods for parabolic differential equations. Int. J. Numer. Methods Engrg. 17 (1981) 335-346.
    • (1981) Int. J. Numer. Methods Engrg. , vol.17 , pp. 335-346
    • Sommeijer, B.P.1    Van Der Houwen, P.J.2    Verwer, J.W.3
  • 31
    • 84968468860 scopus 로고
    • A multi-step formulation of the optimized Lax-Wendroff method for non-linear hyperbolic systems in two space variables
    • A.R. Gourlay and J. Ll. Morris, A multi-step formulation of the optimized Lax-Wendroff method for non-linear hyperbolic systems in two space variables, Math. Comput. 22 (1968) 715-720.
    • (1968) Math. Comput. , vol.22 , pp. 715-720
    • Gourlay, A.R.1    Morris, J.Ll.2
  • 32
    • 0041950967 scopus 로고
    • Boundary techniques for the multistep formulation of the optimized Lax-Wendroff method for non-linear hyperbolic systems in two space dimensions
    • G.R. McGuire and J. Ll. Morris, Boundary techniques for the multistep formulation of the optimized Lax-Wendroff method for non-linear hyperbolic systems in two space dimensions, J. Inst. Math. Applic. 10 (1972) 150-165.
    • (1972) J. Inst. Math. Applic. , vol.10 , pp. 150-165
    • McGuire, G.R.1    Morris, J.Ll.2
  • 33
    • 0024470996 scopus 로고
    • Process splitting of the boundary conditions for the advection-dispersion equation
    • K.O. Aiyesimoju and R.J. Sobey, Process splitting of the boundary conditions for the advection-dispersion equation. Int. J. Numer. Methods Fluids 9 (1989) 235-244.
    • (1989) Int. J. Numer. Methods Fluids , vol.9 , pp. 235-244
    • Aiyesimoju, K.O.1    Sobey, R.J.2
  • 34
    • 0020850440 scopus 로고
    • Fractional step algorithm for estuarine mass transport
    • R.J. Sobey, Fractional step algorithm for estuarine mass transport, Int. J. Numer. Methods Fluids 3 (1983) 567-581.
    • (1983) Int. J. Numer. Methods Fluids , vol.3 , pp. 567-581
    • Sobey, R.J.1
  • 35
    • 0042451519 scopus 로고
    • Accuracy analysis of the backward method of characteristics
    • A.S. Costa et al., eds., Springer-Verlag, Berlin
    • A.M. Baptista, E.E. Adams and K.D. Stolzenbach, Accuracy analysis of the backward method of characteristics, in: A.S. Costa et al., eds., Finite Elements in Water Resources (Springer-Verlag, Berlin, 1986) 477-488.
    • (1986) Finite Elements in Water Resources , pp. 477-488
    • Baptista, A.M.1    Adams, E.E.2    Stolzenbach, K.D.3
  • 36
    • 0000626119 scopus 로고
    • On shape preserving interpolation and semi-Lagrangian transport
    • P.J. Rasch and D.L. Williamson, On shape preserving interpolation and semi-Lagrangian transport, SIAM J. Sci. Stat. Comput. 11 (1990) 656-687.
    • (1990) SIAM J. Sci. Stat. Comput. , vol.11 , pp. 656-687
    • Rasch, P.J.1    Williamson, D.L.2
  • 37
    • 0024813204 scopus 로고
    • Two-dimensional semi-Lagrangian transport with shape-preserving interpolation
    • D.L. Williamson and P.J. Rasch, Two-dimensional semi-Lagrangian transport with shape-preserving interpolation, Mon. Weather Rev. 117 (1989) 102-129.
    • (1989) Mon. Weather Rev. , vol.117 , pp. 102-129
    • Williamson, D.L.1    Rasch, P.J.2
  • 42
    • 0002924166 scopus 로고
    • The remainder of certain linear approximation formulas in two variables
    • D.D. Stancu, The remainder of certain linear approximation formulas in two variables, J. SIAM Numer. Anal. 1 (1964) 137-163.
    • (1964) J. SIAM Numer. Anal. , vol.1 , pp. 137-163
    • Stancu, D.D.1
  • 43
    • 0016872765 scopus 로고
    • On the relationship between the finite element and finite difference methods
    • W.G. Gray and G.F. Pinder, On the relationship between the finite element and finite difference methods, Int. J. Numer. Methods Engrg 10 (1976) 893-923.
    • (1976) Int. J. Numer. Methods Engrg , vol.10 , pp. 893-923
    • Gray, W.G.1    Pinder, G.F.2
  • 44
    • 0019575119 scopus 로고
    • Don't suppress the wiggles - They're telling you something!
    • P.H. Gresho and R.L. Lee, Don't suppress the wiggles - they're telling you something!, Comput. Fluids 9 (1981) 223-253.
    • (1981) Comput. Fluids , vol.9 , pp. 223-253
    • Gresho, P.H.1    Lee, R.L.2


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