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Volumn 25, Issue 1, 2005, Pages 157-194

Fourth-order Runge-Kutta schemes for fluid mechanics applications

Author keywords

Backward differentiation formulae; Convection diffusion reaction; High order; Modified extended efficiency; Runge Kutta; Time discretization; Turbulence

Indexed keywords

FLUID MECHANICS; INTEGRATION; LAMINAR FLOW; NAVIER STOKES EQUATIONS; PROBLEM SOLVING; REYNOLDS NUMBER; TURBULENCE;

EID: 28844509621     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-004-4637-3     Document Type: Conference Paper
Times cited : (78)

References (33)
  • 1
    • 0001266425 scopus 로고
    • Diagonally implicit Runge-Kutta methods for stiff O.D.E.s.
    • Alexander, R. (1977). Diagonally implicit Runge-Kutta methods for stiff O.D.E.s. SIAM J. Num. Anal. 14(6), 1006-1021.
    • (1977) SIAM J. Num. Anal. , vol.14 , Issue.6 , pp. 1006-1021
    • Alexander, R.1
  • 2
    • 0028315726 scopus 로고
    • An implicit upwind algorithm for computing turbulent flows on unstructured grids
    • Anderson, W. K. and Bonhaus, D. L. (1994). An implicit upwind algorithm for computing turbulent flows on unstructured grids. Comp. and Fluids 23(1), 1-21.
    • (1994) Comp. and Fluids , vol.23 , Issue.1 , pp. 1-21
    • Anderson, W.K.1    Bonhaus, D.L.2
  • 3
    • 0001737039 scopus 로고
    • Implicit-explicit methods for time-dependent partial differential equations
    • Ascher, U. M., Ruuth, S. J., and Wetton, B. T. R. (1995). Implicit-explicit methods for time-dependent partial differential equations. SIAM J. Num. Anal. 32(3), 797-823.
    • (1995) SIAM J. Num. Anal. , vol.32 , Issue.3 , pp. 797-823
    • Ascher, U.M.1    Ruuth, S.J.2    Wetton, B.T.R.3
  • 4
    • 0031269714 scopus 로고    scopus 로고
    • Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
    • Ascher, U. M., Ruuth, S. J., and Spiteri, R. J. (1997). Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations. Appl. Num. Math. 25(2-3), 151-167.
    • (1997) Appl. Num. Math. , vol.25 , Issue.2-3 , pp. 151-167
    • Ascher, U.M.1    Ruuth, S.J.2    Spiteri, R.J.3
  • 5
    • 0037054351 scopus 로고    scopus 로고
    • Time integration schemes for the unsteady Navier-stokes equations
    • Bijl, H., Carpenter, M. H., Vatsa, V. N., and Kennedy, C. A. (2002). Time integration schemes for the unsteady Navier-Stokes equations. J. Comp. Phys. 179(1), 313-329.
    • (2002) J. Comp. Phys. , vol.179 , Issue.1 , pp. 313-329
    • Bijl, H.1    Carpenter, M.H.2    Vatsa, V.N.3    Kennedy, C.A.4
  • 7
    • 38249003919 scopus 로고
    • Diagonally-implicit multi-stage integration methods
    • Butcher, J. C. (1993). Diagonally-implicit multi-stage integration methods. Appl. Num. Math. 11(5), 347-363.
    • (1993) Appl. Num. Math. , vol.11 , Issue.5 , pp. 347-363
    • Butcher, J.C.1
  • 8
    • 0012458515 scopus 로고    scopus 로고
    • General linear methods for stiff differential equations
    • Butcher, J. C. (2001). General linear methods for stiff differential equations. BIT 41(2), 240-264.
    • (2001) BIT , vol.41 , Issue.2 , pp. 240-264
    • Butcher, J.C.1
  • 9
    • 0035370920 scopus 로고    scopus 로고
    • Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations
    • Calvo, M. P., de Frutos, J., and Novo, J. (2001). Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations. Appl. Num. Math. 37(4), 535-549.
    • (2001) Appl. Num. Math. , vol.37 , Issue.4 , pp. 535-549
    • Calvo, M.P.1    De Frutos, J.2    Novo, J.3
  • 10
    • 34648879708 scopus 로고    scopus 로고
    • The efficiency of high order temporal schemes
    • 41st Aerospace Sciences Meeting & Exhibit, January 2003, Reno, NV
    • Carpenter, M. H., Viken, S. A., and Nielsen, E. J. (2003). The Efficiency of High Order Temporal Schemes, AIAA-2003-0086, 41st Aerospace Sciences Meeting & Exhibit, January 2003, Reno, NV.
    • (2003) AIAA-2003-0086
    • Carpenter, M.H.1    Viken, S.A.2    Nielsen, E.J.3
  • 11
    • 0001288471 scopus 로고
    • On the integration of stiff systems of O.D.E.'s using extended backward differentiation formulae
    • Cash, J. R. (1980). On the integration of stiff systems of O.D.E.'s using extended backward differentiation formulae. Numer. Math. 34(3), 235-246.
    • (1980) Numer. Math. , vol.34 , Issue.3 , pp. 235-246
    • Cash, J.R.1
  • 12
    • 0020910120 scopus 로고
    • The integration of stiff systems of O.D.E.'s using modified extended backward differentiation formulae
    • Cash, J. R. (1983). The integration of stiff systems of O.D.E.'s using modified extended backward differentiation formulae. Comp. and Math, with Appls. 9(5), 645-657.
    • (1983) Comp. and Math, with Appls. , vol.9 , Issue.5 , pp. 645-657
    • Cash, J.R.1
  • 14
    • 0000687568 scopus 로고
    • A PI-stepsize control for the numerical solution of ordinary differential equations
    • Gustafsson, K., Lundh, M., and Söderlind, G. (1988). A PI-stepsize control for the numerical solution of ordinary differential equations, BIT 28(2), 270-287.
    • (1988) BIT , vol.28 , Issue.2 , pp. 270-287
    • Gustafsson, K.1    Lundh, M.2    Söderlind, G.3
  • 15
    • 0026283488 scopus 로고
    • Control theoretic techniques for stepsize selection in Runge-Kutta methods
    • Gustafsson, K. (1991). Control theoretic techniques for stepsize selection in Runge-Kutta methods. ACM Trans. Math. Soft. 17(4), 533-554.
    • (1991) ACM Trans. Math. Soft. , vol.17 , Issue.4 , pp. 533-554
    • Gustafsson, K.1
  • 16
    • 0028737039 scopus 로고
    • Control theoretic techniques for stepsize selection in implicit Runge-Kutta methods
    • Gustafsson, K. (1994). Control theoretic techniques for stepsize selection in implicit Runge-Kutta methods. ACM Trans. Math. Soft. 20(4), 496-517.
    • (1994) ACM Trans. Math. Soft. , vol.20 , Issue.4 , pp. 496-517
    • Gustafsson, K.1
  • 17
    • 0030621839 scopus 로고    scopus 로고
    • Control strategies for the iterative solution of nonlinear equations in ODE solvers
    • Gustafsson, K., and Söderlind, G. (1997). Control strategies for the iterative solution of nonlinear equations in ODE solvers. SIAM J. Sci. Comput. 18(1), 23-40.
    • (1997) SIAM J. Sci. Comput. , vol.18 , Issue.1 , pp. 23-40
    • Gustafsson, K.1    Söderlind, G.2
  • 18
    • 0001599522 scopus 로고
    • Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations
    • Hairer, E., Lubich, Ch., and Roche, M. (1988). Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations. BIT 28(3), 678-700.
    • (1988) BIT , vol.28 , Issue.3 , pp. 678-700
    • Hairer, E.1    Lubich, Ch.2    Roche, M.3
  • 21
    • 0037216570 scopus 로고    scopus 로고
    • Additive Runge-Kutta schemes for convection-diffusion-reaction equations
    • Kennedy, C. A. and Carpenter, M. H. (2003). Additive Runge-Kutta schemes for convection-diffusion-reaction equations. Appl. Num. Math. 44(1-2), 139-181.
    • (2003) Appl. Num. Math. , vol.44 , Issue.1-2 , pp. 139-181
    • Kennedy, C.A.1    Carpenter, M.H.2
  • 22
    • 0030287581 scopus 로고    scopus 로고
    • Runge-Kutta research in Trondheim
    • Kværnø, A., Nørsett, S. P., and Owren, B. (1996). Runge-Kutta research in Trondheim, Appl. Num. Math. 22(1-3), 263-277.
    • (1996) Appl. Num. Math. , vol.22 , Issue.1-3 , pp. 263-277
    • Kværnø, A.1    Nørsett, S.P.2    Owren, B.3
  • 23
    • 8144227574 scopus 로고    scopus 로고
    • Singly diagonally implicit Runge-Kutta methods with an explicit first stage
    • Kværnø, A. (2004). Singly diagonally implicit Runge-Kutta methods with an explicit first stage, BIT, 44(3), 489-502.
    • (2004) BIT , vol.44 , Issue.3 , pp. 489-502
    • Kværnø, A.1
  • 27
    • 2942757053 scopus 로고
    • Approximate Riemann solvers, parameter vectors, and difference schemes
    • Roe, P. (1981). Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comp. Phys. 43, 357-372.
    • (1981) J. Comp. Phys. , vol.43 , pp. 357-372
    • Roe, P.1
  • 29
    • 0003071240 scopus 로고
    • A one-equation turbulence model for aerodynamic flows
    • 30th Aerospace Sciences Meeting and Exhibit, January 1992, Reno, NV
    • Spalart, P. R. and Allmaras, S. R. (1992). A one-equation turbulence model for aerodynamic flows, AIAA Paper 92-0439, 30th Aerospace Sciences Meeting and Exhibit, January 1992, Reno, NV.
    • (1992) AIAA Paper , vol.92 , Issue.439
    • Spalart, P.R.1    Allmaras, S.R.2
  • 31
    • 0020223604 scopus 로고
    • Flux vector splitting for the Euler equations
    • Krause, E. (ed.), Springer-Verlag, Berlin
    • Van Leer, B. (1982). Flux vector splitting for the Euler equations, In Krause, E. (ed.), Lecture Notes in Physics, 170, Springer-Verlag, Berlin, 501-512.
    • (1982) Lecture Notes in Physics , vol.170 , pp. 501-512
    • Van Leer, B.1
  • 32
    • 0025662592 scopus 로고
    • Development of a multigrid code for 3D Navier-stokes equations and its application to a grid-refinement study
    • Vatsa, V. N. and Wedan, B. W. (1990). Development of a multigrid code for 3D Navier-Stokes equations and its application to a grid-refinement study, Comp. Fluids 18(4), 391-403.
    • (1990) Comp. Fluids , vol.18 , Issue.4 , pp. 391-403
    • Vatsa, V.N.1    Wedan, B.W.2
  • 33
    • 0008455770 scopus 로고
    • Convergence and order reduction of diagonally implicit Runge-Kutta schemes in the method of lines
    • Griffiths D. F., and Watson, G. A. (eds.), Burnt Mill, Harlow, Essex, England: Longman Sci. Tech.; NY.
    • Verwer, J. G. (1986). Convergence and order reduction of diagonally implicit Runge-Kutta schemes in the method of lines. Griffiths D. F., and Watson, G. A. (eds.), Numerical Analysis, Res. Notes in Math. Ser. 140. Burnt Mill, Harlow, Essex, England: Longman Sci. Tech.; NY., 220-237.
    • (1986) Numerical Analysis, Res. Notes in Math. Ser. , vol.140 , pp. 220-237
    • Verwer, J.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.