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Volumn 228, Issue 6, 2009, Pages 2266-2281

Linear high-resolution schemes for hyperbolic conservation laws: TVB numerical evidence

Author keywords

Hyperbolic conservation laws; Numerical methods

Indexed keywords

PARTIAL DIFFERENTIAL EQUATIONS; PHYSICAL PROPERTIES;

EID: 59149103598     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.12.010     Document Type: Article
Times cited : (30)

References (27)
  • 2
    • 0000334985 scopus 로고
    • The Effect of viscosity in hypervelocity impact cratering
    • MacCormack R.W. The Effect of viscosity in hypervelocity impact cratering. AIAA Paper (1969) 69-354
    • (1969) AIAA Paper , pp. 69-354
    • MacCormack, R.W.1
  • 3
    • 0000935266 scopus 로고
    • A difference scheme for numerical solution of discontinuous solution of hydrodynamic equations
    • (Translated US Joint Publ. Res. Service, JPRS 7226, 1969)
    • Godunov S.K. A difference scheme for numerical solution of discontinuous solution of hydrodynamic equations. Math. Sbornik 47 (1959) 271-306 (Translated US Joint Publ. Res. Service, JPRS 7226, 1969)
    • (1959) Math. Sbornik , vol.47 , pp. 271-306
    • Godunov, S.K.1
  • 4
    • 0001328401 scopus 로고
    • Calculation of intersection of non-steady shock waves with obstacles
    • Rusanov V.V. Calculation of intersection of non-steady shock waves with obstacles. J. Comput. Math. Phys. USSR 1 (1961) 267-279
    • (1961) J. Comput. Math. Phys. USSR , vol.1 , pp. 267-279
    • Rusanov, V.V.1
  • 5
    • 40749159424 scopus 로고
    • High resolution schemes for hyperbolic conservation laws
    • Harten A. High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49 (1983) 357-393
    • (1983) J. Comput. Phys. , vol.49 , pp. 357-393
    • Harten, A.1
  • 6
    • 85190567878 scopus 로고    scopus 로고
    • S. Osher, S. Chakrabarthy, Very high order accurate TVD schemes, ICASE Report 84-44, IMA Volumes in Mathematics and its Applications, vol. 2, Springer-Verlag, 1984, 1986, pp. 229-274.
    • S. Osher, S. Chakrabarthy, Very high order accurate TVD schemes, ICASE Report 84-44, IMA Volumes in Mathematics and its Applications, vol. 2, Springer-Verlag, 1984, 1986, pp. 229-274.
  • 7
    • 85190569343 scopus 로고    scopus 로고
    • R.J. LeVeque, Numerical Methods for Conservation Laws, Lectures in Mathematics, Birkhäuser, 1992.
    • R.J. LeVeque, Numerical Methods for Conservation Laws, Lectures in Mathematics, Birkhäuser, 1992.
  • 8
    • 84966251037 scopus 로고
    • TVB uniformly high-order schemes for conservation laws
    • Shu C.-W. TVB uniformly high-order schemes for conservation laws. Math. Comput. 49 (1987) 105-121
    • (1987) Math. Comput. , vol.49 , pp. 105-121
    • Shu, C.-W.1
  • 9
    • 0023329384 scopus 로고
    • Uniformly high-order accurate nonoscillatory schemes, I
    • Harten A., and Osher S. Uniformly high-order accurate nonoscillatory schemes, I. SIAM J. Numer. Anal. 24 (1987) 279-309
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 279-309
    • Harten, A.1    Osher, S.2
  • 10
    • 33749725182 scopus 로고
    • Uniformly high-order accurate essentially non-oscillatory schemes
    • Harten A., Engquist B., Osher S., and Charavarty S. Uniformly high-order accurate essentially non-oscillatory schemes. J. Comput. Phys. 71 (1987) 231-303
    • (1987) J. Comput. Phys. , vol.71 , pp. 231-303
    • Harten, A.1    Engquist, B.2    Osher, S.3    Charavarty, S.4
  • 11
    • 0000897959 scopus 로고    scopus 로고
    • Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy
    • Balsara D.S., and Shu C.-W. Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. J. Comput. Phys. 160 (2000) 405-452
    • (2000) J. Comput. Phys. , vol.160 , pp. 405-452
    • Balsara, D.S.1    Shu, C.-W.2
  • 12
    • 0034190356 scopus 로고    scopus 로고
    • A third order central WENO scheme for 2D conservation laws
    • Levy D., Puppo G., and Russo G. A third order central WENO scheme for 2D conservation laws. Appl. Numer. Math. 33 (2000) 415
    • (2000) Appl. Numer. Math. , vol.33 , pp. 415
    • Levy, D.1    Puppo, G.2    Russo, G.3
  • 13
    • 33745029314 scopus 로고    scopus 로고
    • On the total variation of high-order semi-discrete central schemes for conservation laws
    • Bryson S., and Levy D. On the total variation of high-order semi-discrete central schemes for conservation laws. J. Sci. Comput. 27 (2006) 163
    • (2006) J. Sci. Comput. , vol.27 , pp. 163
    • Bryson, S.1    Levy, D.2
  • 14
    • 0347987814 scopus 로고    scopus 로고
    • New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
    • Kurganov A., and Tadmor E. New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations. J. Comput. Phys. 160 (2000) 214-282
    • (2000) J. Comput. Phys. , vol.160 , pp. 214-282
    • Kurganov, A.1    Tadmor, E.2
  • 15
    • 0034879339 scopus 로고    scopus 로고
    • A third-order semidiscrete central scheme for conservation laws and convection-diffusion equations
    • Kurganov A., and Levy D. A third-order semidiscrete central scheme for conservation laws and convection-diffusion equations. SIAM J. Sci. Comput. 22 (2000) 1461-1488
    • (2000) SIAM J. Sci. Comput. , vol.22 , pp. 1461-1488
    • Kurganov, A.1    Levy, D.2
  • 17
    • 45449125925 scopus 로고
    • Efficient implementation of essentially non-oscillatory shock-capturing schemes
    • Shu C.-W., and Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. v77 (1988) 439-471
    • (1988) J. Comput. Phys. , vol.v77 , pp. 439-471
    • Shu, C.-W.1    Osher, S.2
  • 18
    • 1542576022 scopus 로고    scopus 로고
    • Nonoscillatory high order accurate self-similar maximum principle satisfying shock capturing schemes I
    • Liu X.-d., and Osher S. Nonoscillatory high order accurate self-similar maximum principle satisfying shock capturing schemes I. SIAM J. Numer. Anal. 33 (1996) 439-471
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 439-471
    • Liu, X.-d.1    Osher, S.2
  • 19
    • 2942705023 scopus 로고
    • A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
    • Sod G.A. A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. J. Comput. Phys. 27 (1978) 1-31
    • (1978) J. Comput. Phys. , vol.27 , pp. 1-31
    • Sod, G.A.1
  • 20
    • 84980078953 scopus 로고
    • Weak solutions of nonlinear hyperbolic equations and their numerical computation
    • Lax P.D. Weak solutions of nonlinear hyperbolic equations and their numerical computation. Commun. Pure Appl. Math. 7 (1954) 159193
    • (1954) Commun. Pure Appl. Math. , vol.7 , pp. 159193
    • Lax, P.D.1
  • 21
    • 0018286867 scopus 로고
    • Small-scale structure of two-dimensional magnetohydrodynamic turbulence
    • Orszag S.A., and Tang C.M. Small-scale structure of two-dimensional magnetohydrodynamic turbulence. J. Fluid Mech. 90 1 (1979) 129-143
    • (1979) J. Fluid Mech. , vol.90 , Issue.1 , pp. 129-143
    • Orszag, S.A.1    Tang, C.M.2
  • 22
    • 3142757150 scopus 로고
    • Towards the ultimate conservative difference scheme III. Upstream-centered finite-difference schemes for ideal compressible flow
    • Van Leer B. Towards the ultimate conservative difference scheme III. Upstream-centered finite-difference schemes for ideal compressible flow. J. Comput. Phys. 23 (1977) 263-275
    • (1977) J. Comput. Phys. , vol.23 , pp. 263-275
    • Van Leer, B.1
  • 23
    • 0242679688 scopus 로고    scopus 로고
    • Non-uniform convergence of finite volume schemes for Riemann problems of ideal magnetohydrodynamics
    • Torrilhon M. Non-uniform convergence of finite volume schemes for Riemann problems of ideal magnetohydrodynamics. J. Comput. Phys. 192 (2003) 73-74
    • (2003) J. Comput. Phys. , vol.192 , pp. 73-74
    • Torrilhon, M.1
  • 24
    • 48749139407 scopus 로고
    • The numerical simulation of two-dimensional fluid flow with strong shock
    • Woodward P., and Colella P. The numerical simulation of two-dimensional fluid flow with strong shock. J. Comput. Phys. 54 (1984) 115173
    • (1984) J. Comput. Phys. , vol.54 , pp. 115173
    • Woodward, P.1    Colella, P.2
  • 25
    • 0037431197 scopus 로고    scopus 로고
    • Resolution of high-order WENO schemes for complicated flow structures
    • Shi J., Zhan Y.-T., and Shu C.-W. Resolution of high-order WENO schemes for complicated flow structures. J. Comput. Phys. 186 (2003) 690-696
    • (2003) J. Comput. Phys. , vol.186 , pp. 690-696
    • Shi, J.1    Zhan, Y.-T.2    Shu, C.-W.3
  • 26
    • 1442307691 scopus 로고    scopus 로고
    • Spectral finite volume method for conservation laws on unstructured grids IV: extension to two-dimensional systems
    • Wang Z.J., Zhang L., and Liu Y. Spectral finite volume method for conservation laws on unstructured grids IV: extension to two-dimensional systems. J. Comput. Phys. 194 (2004) 716-741
    • (2004) J. Comput. Phys. , vol.194 , pp. 716-741
    • Wang, Z.J.1    Zhang, L.2    Liu, Y.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.