메뉴 건너뛰기




Volumn 31, Issue 1-2, 2007, Pages 273-305

A new smoothness indicator for the WENO schemes and its effect on the convergence to steady state solutions

Author keywords

Smoothness indicator; Steady state solution; WENO scheme

Indexed keywords

SMOOTHNESS INDICATOR; STEADY STATE SOLUTION; WENO SCHEME;

EID: 34247341292     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-006-9111-y     Document Type: Article
Times cited : (116)

References (22)
  • 1
    • 0035273564 scopus 로고    scopus 로고
    • Strong stability preserving high order time discretization methods
    • Gottlieb, S., Shu, C.-W., and Tadmor, E. (2001). Strong stability preserving high order time discretization methods. SIAM Rev. 43, 89-112.
    • (2001) SIAM Rev , vol.43 , pp. 89-112
    • Gottlieb, S.1    Shu, C.-W.2    Tadmor, E.3
  • 2
    • 40749159424 scopus 로고
    • High-resolution schemes for hyperbolic conservation laws
    • Harten, A. (1983). High-resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49, 357-393.
    • (1983) J. Comput. Phys , vol.49 , pp. 357-393
    • Harten, A.1
  • 3
    • 33749725182 scopus 로고
    • Uniformly high order essentially non-oscillatory schemes, III
    • Harten, A., Engquist, B., Osher, S., and Chakravarthy, S. (1987). Uniformly high order essentially non-oscillatory schemes, III. J. Comput. Phys. 71, 231-303.
    • (1987) J. Comput. Phys , vol.71 , pp. 231-303
    • Harten, A.1    Engquist, B.2    Osher, S.3    Chakravarthy, S.4
  • 4
    • 18844441718 scopus 로고    scopus 로고
    • Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
    • Henrick, A. K., Aslam, T. D., and Powers, J. M. (2005). Mapped weighted essentially non-oscillatory schemes: achieving optimal order near critical points. J. Comput. Phys. 207, 542-567.
    • (2005) J. Comput. Phys , vol.207 , pp. 542-567
    • Henrick, A.K.1    Aslam, T.D.2    Powers, J.M.3
  • 5
    • 0005020603 scopus 로고
    • Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence in transonic and hypersonic flows
    • Jameson, A. (1993). Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence in transonic and hypersonic flows. AIAA Paper 93-3359.
    • (1993) AIAA Paper , pp. 93-3359
    • Jameson, A.1
  • 6
    • 0035245857 scopus 로고    scopus 로고
    • A perspective on computational algorithms for aerodynamic analysis and design
    • Jameson, A. (2001). A perspective on computational algorithms for aerodynamic analysis and design. Prog. Aerosp. Sci. 37, 197-243.
    • (2001) Prog. Aerosp. Sci , vol.37 , pp. 197-243
    • Jameson, A.1
  • 7
    • 0030161771 scopus 로고    scopus 로고
    • Efficient implementation of weighted ENO schemes
    • Jiang, G.-S., and Shu, C.-W. (1996). Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202-228.
    • (1996) J. Comput. Phys , vol.126 , pp. 202-228
    • Jiang, G.-S.1    Shu, C.-W.2
  • 8
    • 0001116632 scopus 로고    scopus 로고
    • A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics
    • Jiang, G.-S., and Wu, C.-C. (1999). A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics. J. Comput. Phys. 150, 561-594.
    • (1999) J. Comput. Phys , vol.150 , pp. 561-594
    • Jiang, G.-S.1    Wu, C.-C.2
  • 9
    • 0000592595 scopus 로고
    • Weighted essentially non-oscillatory schemes
    • Liu, X.-D., Osher, S., and Chan, T. (1994), Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115, 200-212.
    • (1994) J. Comput. Phys , vol.115 , pp. 200-212
    • Liu, X.-D.1    Osher, S.2    Chan, T.3
  • 10
    • 0021513288 scopus 로고
    • High-resolution schemes and the entropy condition
    • Osher, S., and Chakravarthy, C. (1984). High-resolution schemes and the entropy condition. SIAM J. Numer. Anal. 21, 955-984.
    • (1984) SIAM J. Numer. Anal , vol.21 , pp. 955-984
    • Osher, S.1    Chakravarthy, C.2
  • 11
  • 12
    • 1442282989 scopus 로고    scopus 로고
    • Power ENO methods: A fifth-order accurate weighted power ENO method
    • Serna, S., and Marquina, A. (2004). Power ENO methods: a fifth-order accurate weighted power ENO method. J. Comput. Phys. 194, 632-658.
    • (2004) J. Comput. Phys , vol.194 , pp. 632-658
    • Serna, S.1    Marquina, A.2
  • 13
    • 0037431197 scopus 로고    scopus 로고
    • Resolution of high-order WENO schemes for complicated flow structures
    • Shi, J., Zhang, Y.-T., and Shu, C.-W. (2003). Resolution of high-order WENO schemes for complicated flow structures. J. Comput. Phys. 186, 690-696.
    • (2003) J. Comput. Phys , vol.186 , pp. 690-696
    • Shi, J.1    Zhang, Y.-T.2    Shu, C.-W.3
  • 14
    • 0000564951 scopus 로고
    • Total-Variation-Diminishing time discretizations
    • Shu, C.-W. (1988). Total-Variation-Diminishing time discretizations. SIAM J. Sci. Stat. Comput. 9, 1073-1084.
    • (1988) SIAM J. Sci. Stat. Comput , vol.9 , pp. 1073-1084
    • Shu, C.-W.1
  • 15
    • 34247381787 scopus 로고    scopus 로고
    • Shu, C.-W. (1998). Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. In B. Cockburn, C. Johnson, C.-W Shu and E. Tadmor (Editor: A. Quarteroni), Advanced Numerical Approximation of Nonlinear Hyperbolic Equations Lecture Notes in Mathematics, 1697. Springer, Berlin, pp. 325-432.
    • Shu, C.-W. (1998). Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. In B. Cockburn, C. Johnson, C.-W Shu and E. Tadmor (Editor: A. Quarteroni), Advanced Numerical Approximation of Nonlinear Hyperbolic Equations Lecture Notes in Mathematics, Vol. 1697. Springer, Berlin, pp. 325-432.
  • 16
    • 45449125925 scopus 로고
    • Efficient implementation of essentially non-oscillatory shock capturing schemes
    • Shu, C.-W., and Osher, S. (1988). Efficient implementation of essentially non-oscillatory shock capturing schemes. J. Comput. Phys. 77, 439-471.
    • (1988) J. Comput. Phys , vol.77 , pp. 439-471
    • Shu, C.-W.1    Osher, S.2
  • 17
    • 0001568854 scopus 로고
    • Efficient implementation of essentially non- oscillatory shock capturing schemes II
    • Shu, C.-W., and Osher, S. (1989). Efficient implementation of essentially non- oscillatory shock capturing schemes II. J. Comput. Phys. 83, 32-78.
    • (1989) J. Comput. Phys , vol.83 , pp. 32-78
    • Shu, C.-W.1    Osher, S.2
  • 18
    • 2442433925 scopus 로고
    • Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
    • Van Leer, B. (1979). Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method. J. Comput. Phys. 32, 101-136.
    • (1979) J. Comput. Phys , vol.32 , pp. 101-136
    • Van Leer, B.1
  • 19
    • 0040075637 scopus 로고
    • Convergence to steady state solutions of the Euler equations on unstructured grids with limiters
    • Venkatakrishnan, V. (1995). Convergence to steady state solutions of the Euler equations on unstructured grids with limiters. J. Comput. Phys. 118, 120-130.
    • (1995) J. Comput. Phys , vol.118 , pp. 120-130
    • Venkatakrishnan, V.1
  • 20
    • 48749139407 scopus 로고
    • The numerical simulation of two-dimensional fluid flow with strong shocks
    • Woodward, P., and Colella P. (1984). The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54, 115-173.
    • (1984) J. Comput. Phys , vol.54 , pp. 115-173
    • Woodward, P.1    Colella, P.2
  • 21
    • 30044449961 scopus 로고    scopus 로고
    • Multistage interaction of a shock wave and a strong vortex
    • Zhang, S., Zhang, Y.-T., and Shu, C.-W. (2005). Multistage interaction of a shock wave and a strong vortex. Phys. Fluid 17, 116101.
    • (2005) Phys. Fluid , vol.17 , pp. 116101
    • Zhang, S.1    Zhang, Y.-T.2    Shu, C.-W.3
  • 22
    • 0346304850 scopus 로고    scopus 로고
    • Numerical viscosity and resolution of high-order weighted essentially nonoscillatory schemes for compressible flows with high Reynolds numbers
    • Zhang, Y.-T., Shi, J., Shu, C.-W., and Zhou, Y. (2003). Numerical viscosity and resolution of high-order weighted essentially nonoscillatory schemes for compressible flows with high Reynolds numbers. Phys. Rev. E 68, 046709.
    • (2003) Phys. Rev. E , vol.68 , pp. 046709
    • Zhang, Y.-T.1    Shi, J.2    Shu, C.-W.3    Zhou, Y.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.