메뉴 건너뛰기




Volumn 25, Issue 4, 2009, Pages 810-832

Application of Richardson extrapolation to the numerical solution of partial differential equations

Author keywords

Defect correction method; Higher order methods; Order of accuracy; Richardson extrapolation

Indexed keywords


EID: 67849135000     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20375     Document Type: Article
Times cited : (39)

References (27)
  • 1
    • 0003757884 scopus 로고    scopus 로고
    • Numerical mathematics and computation
    • 1 W. Cheney and D. Kincaid, Numerical mathematics and computation, 5th Ed., Brooks/Cole‐Thomson Learning, Belmont, CA, 2004.
    • (2004)
    • Cheney, W.1    Kincaid, D.2
  • 2
    • 85120589921 scopus 로고
    • Semidirect high order accuracy solutions in non‐orthogonal grids by Richardson extrapolation, Fundamentals of computational fluid dynamics
    • 2 P. J. Roache, Semidirect high order accuracy solutions in non‐orthogonal grids by Richardson extrapolation, Fundamentals of computational fluid dynamics, Hermosa Publisher, Albuquerque, NM, 1985.
    • (1985)
    • Roache, P.J.1
  • 3
    • 0344208252 scopus 로고
    • Scaling of high reynolds number weakly separated channel flows, in: Proceedings: Symposium on Numerical and Physical Aspects of Aerodynamic Flows
    • 3 P. J. Roache, Scaling of high reynolds number weakly separated channel flows, T. Cebeci, editor, Proceedings: Symposium on Numerical and Physical Aspects of Aerodynamic Flows, California State University, Long Beach, 1981.
    • (1981)
    • Roache, P.J.1
  • 5
    • 0031176303 scopus 로고    scopus 로고
    • Completed Richardson extrapolation in space and time
    • 5 S. A. Richards, Completed Richardson extrapolation in space and time, Commun Numer Methods Eng 13 ( 1997), 573–582.
    • (1997) Commun Numer Methods Eng , vol.13 , pp. 573-582
    • Richards, S.A.1
  • 6
    • 0347592775 scopus 로고    scopus 로고
    • A high‐order finite difference discretization strategy based on extrapolation for convection diffusion equations
    • 6 H. Sun and J. Zhang, A high‐order finite difference discretization strategy based on extrapolation for convection diffusion equations, Numer Methods Partial Differential Eq 20 ( 2004), 18–32.
    • (2004) Numer Methods Partial Differential Eq , vol.20 , pp. 18-32
    • Sun, H.1    Zhang, J.2
  • 7
    • 33745580052 scopus 로고
    • The defect correction principle and discretization methods
    • 7 H. Stetter, The defect correction principle and discretization methods, Numer Math 29 ( 1978), 425–443.
    • (1978) Numer Math , vol.29 , pp. 425-443
    • Stetter, H.1
  • 8
    • 85120589049 scopus 로고
    • Local defect correction method and domain decomposition techniques, in: Defect correction methods
    • 8 W. Hackbusch, Local defect correction method and domain decomposition techniques, K. Bohmer, H. J. Stetter, editors, Defect correction methods, Springer‐Verlag, Wien and New York, 1984.
    • (1984)
    • Hackbusch, W.1
  • 9
    • 85120593623 scopus 로고
    • Mixed defect correction iteration for the solution of a singular perturbation problem, in: Defect correction methods
    • 9 P. W. Hemker, Mixed defect correction iteration for the solution of a singular perturbation problem, K. Bohmer, H. J. Stetter, editors, Defect correction methods, Springer‐Verlag, Wien and New York, 1984.
    • (1984)
    • Hemker, P.W.1
  • 10
    • 33748549604 scopus 로고    scopus 로고
    • Solving parabolic problems using local defect correction in combination with the finite volume method
    • 10 R. Minero, M. J. H. Anthonissen, and R. M. M. Mattheij, Solving parabolic problems using local defect correction in combination with the finite volume method, Numer Methods Partial Differential Eq 22 ( 2006), 1149–1172.
    • (2006) Numer Methods Partial Differential Eq , vol.22 , pp. 1149-1172
    • Minero, R.1    Anthonissen, M.J.H.2    Mattheij, R.M.M.3
  • 11
  • 12
    • 0345834874 scopus 로고    scopus 로고
    • An investigation of parallel implicit solution algorithms for incompressible flows on multi‐element unstructured topologies
    • 12 D. G. Hyams, K. Sreenivas, C. Sheng, W. R. Briley, D. L. Marcum, and D. L. Whitfield, An investigation of parallel implicit solution algorithms for incompressible flows on multi‐element unstructured topologies, 38th AIAA Aerospace Sciences Meeting, AIAA Paper 2000‐0271, Reno, Nevada, 2000.
    • (2000)
    • Hyams, D.G.1    Sreenivas, K.2    Sheng, C.3    Briley, W.R.4    Marcum, D.L.5    Whitfield, D.L.6
  • 13
    • 85120590435 scopus 로고    scopus 로고
    • 13 http://www.fun3d.com.
  • 14
    • 84884972203 scopus 로고    scopus 로고
    • The spectral difference method for the 2D Euler equations on unstructured grids
    • 14 Z. J. Wang and Y. Liu, The spectral difference method for the 2D Euler equations on unstructured grids, 17th AIAA Computational Fluid Dynamics Conference, AIAA Paper 2005‐5112, Toronto, 2005.
    • (2005)
    • Wang, Z.J.1    Liu, Y.2
  • 15
    • 35649020571 scopus 로고    scopus 로고
    • High‐order accurate methods for high‐speed flow
    • 15 G. May and A. Jameson, High‐order accurate methods for high‐speed flow, 17th AIAA Computational Fluid Dynamics Conference, AIAA Paper 2005‐5251, Toronto, 2005.
    • (2005)
    • May, G.1    Jameson, A.2
  • 16
    • 85120587263 scopus 로고    scopus 로고
    • High‐order spectral volume method for benchmark aeroacoustic problems
    • 16 Z. J. Wang, High‐order spectral volume method for benchmark aeroacoustic problems, 41st AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2003‐0880, Reno, 2003.
    • (2003)
    • Wang, Z.J.1
  • 17
    • 85120589431 scopus 로고    scopus 로고
    • Higher‐order accurate residual‐distribution schemes for unsteady Euler equations on unstructured grids
    • 17 P. DePalma, G. Pascazio, G. Rossiello, and M. Napolitano, Higher‐order accurate residual‐distribution schemes for unsteady Euler equations on unstructured grids, 17th AIAA Computational Fluid Dynamics Conference, AIAA Paper 2005‐5112, Toronto, 2005.
    • (2005)
    • DePalma, P.1    Pascazio, G.2    Rossiello, G.3    Napolitano, M.4
  • 18
    • 33750566897 scopus 로고    scopus 로고
    • High‐order unstructured essentially nonoscillatory and weighted essentially nonoscillatory schemes for aerodynamic flows
    • 18 W. R. Wolf and J. L. F. Azevedo, High‐order unstructured essentially nonoscillatory and weighted essentially nonoscillatory schemes for aerodynamic flows, AIAA J 44 ( 2006), 2295–2310.
    • (2006) AIAA J , vol.44 , pp. 2295-2310
    • Wolf, W.R.1    Azevedo, J.L.F.2
  • 19
    • 85085774626 scopus 로고    scopus 로고
    • Unstructured nonlinear free surface flow solutions: validation and verification
    • 19 C. O. E. Burg, K. Sreenivas, D. G. Hyams, and B. B. Mitchell, Unstructured nonlinear free surface flow solutions: validation and verification, 32nd AIAA Fluid Dynamics Conference, AIAA Paper 2002‐2977, St. Louis, 2002.
    • (2002)
    • Burg, C.O.E.1    Sreenivas, K.2    Hyams, D.G.3    Mitchell, B.B.4
  • 20
    • 85120596190 scopus 로고    scopus 로고
    • 20 L. Eca and M. Hoekstra, An evaluation of verification procedures for CFD applications, Proceedings of the 24th Symposium on Naval Hydrodynamics, Vol. III, Fukuoka, Japan, 2002.
    • (2002) , vol.III
    • Eca, L.1    Hoekstra, M.2
  • 21
    • 34250863776 scopus 로고    scopus 로고
    • Higher order variable extrapolation for unstructured finite volume RANS flow solvers
    • 21 C. O. E. Burg, Higher order variable extrapolation for unstructured finite volume RANS flow solvers, 17th AIAA Computational Fluid Dynamics Conference, AIAA Paper 2005‐4999, Toronto, 2005.
    • (2005)
    • Burg, C.O.E.1
  • 22
    • 34250900695 scopus 로고    scopus 로고
    • Parsing the results of the second drag prediction workshop
    • 22 T. J. Baker, Parsing the results of the second drag prediction workshop, 23rd AIAA Applied Aerodynamics Conference, AIAA Paper 2005‐4731, Toronto, 2005.
    • (2005)
    • Baker, T.J.1
  • 23
    • 49549156305 scopus 로고
    • The modified equation approach to the stability and accuracy analysis of finite‐difference methods
    • 23 R. F. Warming and B. J. Hyett, The modified equation approach to the stability and accuracy analysis of finite‐difference methods, J Comput Phys 14 ( 1974), 159–179.
    • (1974) J Comput Phys , vol.14 , pp. 159-179
    • Warming, R.F.1    Hyett, B.J.2
  • 24
    • 0003767428 scopus 로고
    • Open‐channel flow
    • 24 M. H. Chaudhry, Open‐channel flow, Prentice‐Hall, Englewood Cliffs, NJ, 1993.
    • (1993)
    • Chaudhry, M.H.1
  • 25
    • 0021507758 scopus 로고
    • Symbolic manipulation and computational fluid dynamics
    • 25 S. Steinberg and P. J. Roache, Symbolic manipulation and computational fluid dynamics, AIAA J 22 ( 1984), 1390–1394.
    • (1984) AIAA J , vol.22 , pp. 1390-1394
    • Steinberg, S.1    Roache, P.J.2
  • 26
    • 10844287916 scopus 로고
    • Methodology for computational fluid dynamics: code verification/validation
    • 26 W. L. Oberkampf, F. G. Blottner, and D. P. Aeschliman, Methodology for computational fluid dynamics: code verification/validation, AIAA Paper No. 95‐2226, 26th AIAA Fluid Dynamics Conference, San Diego, 1995.
    • (1995)
    • Oberkampf, W.L.1    Blottner, F.G.2    Aeschliman, D.P.3
  • 27
    • 68549136773 scopus 로고    scopus 로고
    • Numerical solution of the shallow water equations
    • 27 D. L. Whitfield, Numerical solution of the shallow water equations, Mississippi State University Technical Report, MSSU‐EIRS‐ERC‐96‐4, July, 1996.
    • (1996)
    • Whitfield, D.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.