메뉴 건너뛰기




Volumn 36, Issue 5, 1998, Pages 712-724

Aspects of numerical uncertainties in time marching to steady-state numerical solutions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0000761492     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/2.459     Document Type: Article
Times cited : (21)

References (74)
  • 1
    • 0000898792 scopus 로고    scopus 로고
    • Experimental Methodology for Computational Fluid Dynamics Code Validation
    • Aeschliman, D. P., and Oberkampf, W. L., "Experimental Methodology for Computational Fluid Dynamics Code Validation," AIAA Journal, Vol. 36, No. 5, 1998, pp. 733-741.
    • (1998) AIAA Journal , vol.36 , Issue.5 , pp. 733-741
    • Aeschliman, D.P.1    Oberkampf, W.L.2
  • 13
    • 85007708234 scopus 로고
    • A Suggestion for the Numerical Solution of the Steady Navier-Stokes Equations
    • Crocco, L., "A Suggestion for the Numerical Solution of the Steady Navier-Stokes Equations," AIAA Journal, Vol. 3, No. 10, 1965, pp. 1824-1832.
    • (1965) AIAA Journal , vol.3 , Issue.10 , pp. 1824-1832
    • Crocco, L.1
  • 14
    • 0000571441 scopus 로고
    • A Time-Dependent Computational Method for Blunt Body Flows
    • Moretti, G., and Abbett, M., "A Time-Dependent Computational Method for Blunt Body Flows," AIAA Journal, Vol. 4, No. 12, 1966, pp. 2136-2141.
    • (1966) AIAA Journal , vol.4 , Issue.12 , pp. 2136-2141
    • Moretti, G.1    Abbett, M.2
  • 16
    • 0017955203 scopus 로고
    • An Implicit Factored Scheme for the Compressible Navier-Stokes Equations
    • Beam, R. M., and Warming, R. F., "An Implicit Factored Scheme for the Compressible Navier-Stokes Equations," AIAA Journal, Vol. 16, No. 4, 1978, pp. 293-302.
    • (1978) AIAA Journal , vol.16 , Issue.4 , pp. 293-302
    • Beam, R.M.1    Warming, R.F.2
  • 17
    • 0001493254 scopus 로고
    • Solution of the Multidimensional Compressible Navier-Stokes Equations by a Generalized Implicit Method
    • Briley, W. R., and McDonald, H., "Solution of the Multidimensional Compressible Navier-Stokes Equations by a Generalized Implicit Method," Journal of Computational Physics, Vol. 24, 1977, pp. 372-397.
    • (1977) Journal of Computational Physics , vol.24 , pp. 372-397
    • Briley, W.R.1    McDonald, H.2
  • 18
    • 0017994032 scopus 로고
    • Implicit Finite-Difference Simulation of Flow about Arbitrary Two-Dimensional Geometries
    • Steger, J., "Implicit Finite-Difference Simulation of Flow About Arbitrary Two-Dimensional Geometries," AIAA Journal, Vol. 16, No. 7, 1978, pp. 679-686.
    • (1978) AIAA Journal , vol.16 , Issue.7 , pp. 679-686
    • Steger, J.1
  • 20
    • 0003639526 scopus 로고
    • A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods
    • March 6-10, also NASA TM-101088, Feb. 1989
    • Yee, H. C., "A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods," von Kármán Inst. (VKI) for Fluid Dynamics Lecture Series 1989-04, March 6-10, 1989; also NASA TM-101088, Feb. 1989.
    • (1989) Von Kármán Inst. (VKI) for Fluid Dynamics Lecture Series 1989-04
    • Yee, H.C.1
  • 22
    • 3042829361 scopus 로고
    • Yee, H. C., Sweby, P. K., and Griffiths, D. F., "Dynamical Approach Study of Spurious Steady-State Numerical Solutions for Nonlinear Differential Equations, Part I: The Dynamics of Time Discretizations and Its Implications for Algorithm Development in Computational Fluid Dynamics," NASA TM-102820, April 1990; also Journal of Computational Physics, Vol. 97, 1991, pp. 249-310.
    • (1991) Journal of Computational Physics , vol.97 , pp. 249-310
  • 24
    • 0344375578 scopus 로고
    • Yee, H. C., and Sweby, P. K., "Global Asymptotic Behavior of Iterative Implicit Schemes," NASA RIACS TR 93.11, Dec. 1993; also International Journal of Bifurcation and Chaos, Vol. 4, 1994, pp. 1579-1611.
    • (1994) International Journal of Bifurcation and Chaos , vol.4 , pp. 1579-1611
  • 25
    • 84954811121 scopus 로고
    • Dynamical Approach Study of Spurious Steady-State Numerical Solutions for Nonlinear Differential Equations, Part II: Global Asymptotic Behavior of Time Discretizations
    • March
    • Yee, H. C., and Sweby, P. K., "Dynamical Approach Study of Spurious Steady-State Numerical Solutions for Nonlinear Differential Equations, Part II: Global Asymptotic Behavior of Time Discretizations," NASA Rept. RNR-92-008, March 1992; also International Journal of CFD, Vol. 4, 1995, pp. 219-283.
    • (1992) NASA Rept. RNR-92-008
    • Yee, H.C.1    Sweby, P.K.2
  • 26
    • 84954811121 scopus 로고
    • Yee, H. C., and Sweby, P. K., "Dynamical Approach Study of Spurious Steady-State Numerical Solutions for Nonlinear Differential Equations, Part II: Global Asymptotic Behavior of Time Discretizations," NASA Rept. RNR-92-008, March 1992; also International Journal of CFD, Vol. 4, 1995, pp. 219-283.
    • (1995) International Journal of CFD , vol.4 , pp. 219-283
  • 30
    • 0013537451 scopus 로고    scopus 로고
    • Lafon, A., and Yee, H. C., "Dynamical Approach Study of Spurious Steady-State Numerical Solutions for Nonlinear Differential Equations, Part III: The Effects of Nonlinear Source Terms in Reaction-Convection Equations," NASA TM 103877, July 1991; also International Journal of CFD. Vol. 6, 1996, pp. 1-36.
    • (1996) International Journal of CFD , vol.6 , pp. 1-36
  • 32
    • 3142624971 scopus 로고    scopus 로고
    • Lafon, A., and Yee, H. C., "Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations, Part IV: Stability vs. Numerical Treatment of Nonlinear Source Terms," ONERACERT TR DERAT 45/5005.38; also International Journal of CFD, Vol. 6, 1996, pp. 89-123.
    • (1996) International Journal of CFD , vol.6 , pp. 89-123
  • 34
    • 44949266287 scopus 로고
    • Review of Preconditioning Methods for Fluid Dynamics
    • Turkel, E., "Review of Preconditioning Methods for Fluid Dynamics," Applied Numerical Mathematics, Vol. 12, 1993, pp. 257-284.
    • (1993) Applied Numerical Mathematics , vol.12 , pp. 257-284
    • Turkel, E.1
  • 36
    • 0022693323 scopus 로고
    • Linearized Form of Implicit TVD Schemes for Multidimensional Euler and Navier-Stokes Equations
    • Yee, H. C., "Linearized Form of Implicit TVD Schemes for Multidimensional Euler and Navier-Stokes Equations," Computers and Mathematics with Applications, Vol. 12A, 1986, pp. 413-432.
    • (1986) Computers and Mathematics with Applications , vol.12 A , pp. 413-432
    • Yee, H.C.1
  • 37
    • 28144443157 scopus 로고
    • High-Resolution Shock-Capturing Schemes for Inviscid and Viscous Hypersonic Flows
    • Yee, H. C., Klopfer, G. H., and Montagne, J.-L., "High-Resolution Shock-Capturing Schemes for Inviscid and Viscous Hypersonic Flows," Journal of Computational Physics, Vol. 88, 1990, pp. 31-61.
    • (1990) Journal of Computational Physics , vol.88 , pp. 31-61
    • Yee, H.C.1    Klopfer, G.H.2    Montagne, J.-L.3
  • 38
    • 0039939074 scopus 로고
    • On High-Order Accurate Interpolation for Non-Oscillatory Shock-Capturing Schemes
    • Springer-Verlag, Berlin
    • Harten, A., "On High-Order Accurate Interpolation for Non-Oscillatory Shock-Capturing Schemes," The IMA Volumes in Mathematics and Its Applications, Vol. 2, Springer-Verlag, Berlin, 1986, pp. 71-106.
    • (1986) The IMA Volumes in Mathematics and Its Applications , vol.2 , pp. 71-106
    • Harten, A.1
  • 39
    • 0023329384 scopus 로고
    • Uniformly High-Order Accurate Nonoscillatory Schemes I
    • Harten, A., and Osher, S., "Uniformly High-Order Accurate Nonoscillatory Schemes I," SIAM Journal an Numerical Analysis, Vol. 24, 1987, pp. 279-309.
    • (1987) SIAM Journal An Numerical Analysis , vol.24 , pp. 279-309
    • Harten, A.1    Osher, S.2
  • 41
    • 0028446617 scopus 로고
    • Studies on Error Propagation for Certain Nonlinear Approximations to Hyperbolic Equations: Discontinuities in Derivatives
    • Donat, R., "Studies on Error Propagation for Certain Nonlinear Approximations to Hyperbolic Equations: Discontinuities in Derivatives," SIAM Journal on Numerical Analysis, Vol. 31, 1994, pp. 655-679.
    • (1994) SIAM Journal on Numerical Analysis , vol.31 , pp. 655-679
    • Donat, R.1
  • 43
    • 0002519499 scopus 로고
    • Efficient Solution of the Steady Euler Equations with a Centered Implicit Method
    • edited by K. W. Morton and M. J. Baines, Clarendon, Oxford, England, UK
    • Lerat, A., and Sides, J., "Efficient Solution of the Steady Euler Equations with a Centered Implicit Method," Numerical Methods for Fluid Dynamics III, edited by K. W. Morton and M. J. Baines, Clarendon, Oxford, England, UK, 1988, pp. 65-86.
    • (1988) Numerical Methods for Fluid Dynamics III , pp. 65-86
    • Lerat, A.1    Sides, J.2
  • 45
    • 11644259271 scopus 로고
    • On Spurious Steady-State Solutions of Explicit Runge-Kutta Schemes
    • Univ, of Reading, Reading, England, UK; also NASA TM 102819, March
    • Sweby, P. K., Yee, H. C., and Griffiths, D. F., "On Spurious Steady-State Solutions of Explicit Runge-Kutta Schemes," Dept. of Mathematics, Numerical Analysis Rept. 3/90, Univ, of Reading, Reading, England, UK; also NASA TM 102819, March 1990.
    • (1990) Dept. of Mathematics, Numerical Analysis Rept. 3/90
    • Sweby, P.K.1    Yee, H.C.2    Griffiths, D.F.3
  • 46
    • 84954710527 scopus 로고
    • On Spurious Asymptotic Numerical Solutions of 2 × 2 Systems of ODEs
    • Univ. of Reading, Reading, England, UK
    • Sweby, P. K., and Yee, H. C., "On Spurious Asymptotic Numerical Solutions of 2 × 2 Systems of ODEs," Dept. of Mathematics, Numerical Analysis Rept. 7/91, Univ. of Reading, Reading, England, UK, 1991.
    • (1991) Dept. of Mathematics, Numerical Analysis Rept. 7/91
    • Sweby, P.K.1    Yee, H.C.2
  • 48
    • 0042124751 scopus 로고
    • Some Stability Aspects of Schemes for the Adaptive Integration of Stiff Initial Value Problems
    • Dieci, L., and Estep, D., "Some Stability Aspects of Schemes for the Adaptive Integration of Stiff Initial Value Problems," SIAM Journal on Scientific and Statistical Computing, Vol. 12, 1991, pp. 1284-1303.
    • (1991) SIAM Journal on Scientific and Statistical Computing , vol.12 , pp. 1284-1303
    • Dieci, L.1    Estep, D.2
  • 50
    • 0000305898 scopus 로고
    • Computational Chaos - A Prelude to Computational Instability
    • Lorenz, E. N., "Computational Chaos - A Prelude to Computational Instability," Physica D, Vol. 35, 1989, pp. 299-317.
    • (1989) Physica D , vol.35 , pp. 299-317
    • Lorenz, E.N.1
  • 53
    • 0012500963 scopus 로고
    • What Good Are Numerical Simulations of Chaotic Dynamical Systems?
    • Corless, R. M., "What Good Are Numerical Simulations of Chaotic Dynamical Systems?," Computers and Mathematical Applications. Vol. 28, 1994, pp. 107-121.
    • (1994) Computers and Mathematical Applications , vol.28 , pp. 107-121
    • Corless, R.M.1
  • 54
    • 6244274663 scopus 로고
    • Periodic Solutions: Enclosure, Verification, and Applications
    • Academic, New York
    • Adams, E., "Periodic Solutions: Enclosure, Verification, and Applications," Computer Arithmetic and Self-Validating Numerical Methods, Academic, New York, 1990, pp. 199-245.
    • (1990) Computer Arithmetic and Self-Validating Numerical Methods , pp. 199-245
    • Adams, E.1
  • 55
    • 0542363767 scopus 로고
    • The Reliability of Numerical Experiments: Transitions to Chaos in Thermosolutal Convection
    • Moore, D. R., Weiss, N. O., and Wilkins, J. M., The Reliability of Numerical Experiments: Transitions to Chaos in Thermosolutal Convection," Nonlinearity, Vol. 3, 1990, pp. 997-1014.
    • (1990) Nonlinearity , vol.3 , pp. 997-1014
    • Moore, D.R.1    Weiss, N.O.2    Wilkins, J.M.3
  • 56
    • 11644261092 scopus 로고
    • edited by B. D. Sleeman and R. J. Jarvis, Pitmann Research Notes 157, Longman Sci. Tech., Harlow
    • Keener, J. P., Ordinary and Partial Differential Equations, edited by B. D. Sleeman and R. J. Jarvis, Pitmann Research Notes 157, Longman Sci. Tech., Harlow, 1987, pp. 95-112.
    • (1987) Ordinary and Partial Differential Equations , pp. 95-112
    • Keener, J.P.1
  • 57
    • 0012349493 scopus 로고
    • Crises, Sudden Changes in Chaotic Attractors, and Transient Chaos
    • Grebogi, C., Ott, E., and Yorke, J. A., "Crises, Sudden Changes in Chaotic Attractors, and Transient Chaos," Physica 7D, 1983, pp 181-200.
    • (1983) Physica , vol.7 D , pp. 181-200
    • Grebogi, C.1    Ott, E.2    Yorke, J.A.3
  • 63
    • 0039862596 scopus 로고
    • High Order Shock Capturing Methods
    • edited by M. Hafez and K. Oshima, Wiley, New York
    • Engquist, B., and Sjogreen, B., "High Order Shock Capturing Methods," CFD Reviews, edited by M. Hafez and K. Oshima, Wiley, New York, 1995, pp. 210-233.
    • (1995) CFD Reviews , pp. 210-233
    • Engquist, B.1    Sjogreen, B.2
  • 64
    • 84968520219 scopus 로고
    • On Difference Approximations with Wrong Boundary Values
    • Kreiss, H.-O., and Lundqvist, E., "On Difference Approximations with Wrong Boundary Values," Mathematics of Computation, Vol. 22, 1968, pp. 1-12.
    • (1968) Mathematics of Computation , vol.22 , pp. 1-12
    • Kreiss, H.-O.1    Lundqvist, E.2
  • 65
    • 40749083379 scopus 로고
    • Implicit Total Variation Diminishing (TVD) Schemes for Steady-State Calculations
    • Yee, H. C., Warming, R. F., and Harten, A., "Implicit Total Variation Diminishing (TVD) Schemes for Steady-State Calculations," Journal of Computational Physics, Vol. 57, 1985, pp. 327-360.
    • (1985) Journal of Computational Physics , vol.57 , pp. 327-360
    • Yee, H.C.1    Warming, R.F.2    Harten, A.3
  • 66
    • 0023295524 scopus 로고
    • Implicit TVD Schemes for Hyperbolic Conservation Laws in Curvilinear Coordinates
    • also AIAA Paper 85-1513, July 1985
    • Yee, H. C., and Harten, A., "Implicit TVD Schemes for Hyperbolic Conservation Laws in Curvilinear Coordinates," AIAA Journal, Vol. 25, No. 2, 1987, pp. 266-274: also AIAA Paper 85-1513, July 1985.
    • (1987) AIAA Journal , vol.25 , Issue.2 , pp. 266-274
    • Yee, H.C.1    Harten, A.2
  • 67
    • 3142640263 scopus 로고
    • A Dynamical Approach Study of Some Explicit and Implicit TVD Schemes and Their Convergence to Steady-State Solutions
    • Univ. of Reading, England, UK
    • Burton, P. A., and Sweby, P. K., "A Dynamical Approach Study of Some Explicit and Implicit TVD Schemes and Their Convergence to Steady-State Solutions," Dept. of Mathematics, Numerical Analysis Rept. 5/95, Univ. of Reading, England, UK, 1995.
    • (1995) Dept. of Mathematics, Numerical Analysis Rept. 5/95
    • Burton, P.A.1    Sweby, P.K.2
  • 69
    • 0021513424 scopus 로고
    • High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
    • Sweby, P. K., "High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws," SIAM Journal on Numerical Analysis, Vol. 21, 1984, pp. 995-1011.
    • (1984) SIAM Journal on Numerical Analysis , vol.21 , pp. 995-1011
    • Sweby, P.K.1
  • 70
    • 0000882461 scopus 로고
    • Moving Mesh Techniques Based upon Equidistribution and Their Stability,"
    • Ren, Y., and Russell, R. D., "Moving Mesh Techniques Based upon Equidistribution and Their Stability," SIAM Journal on Scientific and Statistical Computing, Vol. 13, 1992, pp. 1265-1286.
    • (1992) SIAM Journal on Scientific and Statistical Computing , vol.13 , pp. 1265-1286
    • Ren, Y.1    Russell, R.D.2
  • 74
    • 0003521454 scopus 로고
    • AUTO: Software for Continuation and Bifurcation Problems in Ordinary Differential Equations
    • Pasadena, CA
    • Doedel, E., "AUTO: Software for Continuation and Bifurcation Problems in Ordinary Differential Equations," California Inst. of Technology, Rept., Pasadena, CA, 1986.
    • (1986) California Inst. of Technology, Rept.
    • Doedel, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.