메뉴 건너뛰기




Volumn 24, Issue 2, 2003, Pages 480-506

A fourth-order central weno scheme for multidimensional hyperbolic systems of conservation laws

Author keywords

Central difference schemes; Central weighted essentially nonoscillatory reconstruction; High order accuracy; Hyperbolic systems; Nonoscillatory schemes; Weighted essentially nonoscillatory reconstruction

Indexed keywords

BOUNDARY CONDITIONS; POLYNOMIALS; PROBLEM SOLVING;

EID: 0037249089     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827501385852     Document Type: Article
Times cited : (142)

References (39)
  • 1
    • 0034450587 scopus 로고    scopus 로고
    • Extended hydrodynamical model of carrier transport in semiconductors
    • A. M. ANILE, V. ROMANO, AND G. Russo, Extended hydrodynamical model of carrier transport in semiconductors, SIAM J. Appl. Math., 61 (2000), pp. 74-101.
    • (2000) SIAM J. Appl. Math. , vol.61 , pp. 74-101
    • Anile, A.M.1    Romano, V.2    Russo, G.3
  • 2
    • 0001884854 scopus 로고
    • A two-dimensional finite volume, extension of the Lax-Friedrichs and Nessyahu-Tadmor schemes for compressible flow
    • Lake Tahoe, NV, M. Hafez and K. Oshima, eds.
    • P. ARMINJON, D. STANESCU, AND M.-C. VIALLON, A two-dimensional finite volume, extension of the Lax-Friedrichs and Nessyahu-Tadmor schemes for compressible flow, in Proceedings of the 6th International Symposium on Computational Fluid Dynamics, Vol. IV, Lake Tahoe, NV, 1995, M. Hafez and K. Oshima, eds., pp. 7-14.
    • (1995) Proceedings of the 6th International Symposium on Computational Fluid Dynamics , vol.4 , pp. 7-14
    • Arminjon, P.1    Stanescu, D.2    Viallon, M.-C.3
  • 3
    • 0033296324 scopus 로고    scopus 로고
    • High-order central schemes for hyperbolic systems of conservation laws
    • F. BIANCO, G. PUPPO, AND G. RUSSO, High-order central schemes for hyperbolic systems of conservation laws, SIAM J. Sci. Comput., 21 (1999), pp. 294-322.
    • (1999) SIAM J. Sci. Comput. , vol.21 , pp. 294-322
    • Bianco, F.1    Puppo, G.2    Russo, G.3
  • 4
    • 85160598111 scopus 로고    scopus 로고
    • High order central schemes for hyperbolic systems of conservation laws
    • Birkhäuser Verlag, Basel, Switzerland
    • F. BIANCO, G. PUPPO, AND G. RUSSO, High Order Central Schemes for Hyperbolic Systems of Conservation Laws, Internat. Ser. Numer. Math. 129, Birkhäuser Verlag, Basel, Switzerland, 1999.
    • (1999) Internat. Ser. Numer. Math. , vol.129
    • Bianco, F.1    Puppo, G.2    Russo, G.3
  • 5
    • 0001380483 scopus 로고
    • Systems of conservation equations with a convex extension
    • K. O. FRIEDRICHS AND P. D. LAX, Systems of conservation equations with a convex extension, Proc. Nat. Acad. Sci. USA, 68 (1971), pp. 1686-1688.
    • (1971) Proc. Nat. Acad. Sci. USA , vol.68 , pp. 1686-1688
    • Friedrichs, K.O.1    Lax, P.D.2
  • 7
    • 33749725182 scopus 로고
    • Uniformly high order accurate essentially non-oscillatory schemes III
    • A. HARTEN, B. ENGQUIST, S. OSHER, AND S. CHAKRAVARTHY, Uniformly high order accurate essentially non-oscillatory schemes III, J. Comput. Phys., 71 (1987), pp. 231-303.
    • (1987) J. Comput. Phys. , vol.71 , pp. 231-303
    • Harten, A.1    Engquist, B.2    Osher, S.3    Chakravarthy, S.4
  • 8
    • 0030161771 scopus 로고    scopus 로고
    • Efficient implementation of weighted ENO schemes
    • G.-S. JIANG AND C.-W. SHU, Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126 (1996), pp. 202-228.
    • (1996) J. Comput. Phys. , vol.126 , pp. 202-228
    • Jiang, G.-S.1    Shu, C.-W.2
  • 9
    • 0032206542 scopus 로고    scopus 로고
    • Nonoscillatory central schemes for multidimensional hyperbolic conservation laws
    • G.-S. JIANG AND E. TADMOR, Nonoscillatory central schemes for multidimensional hyperbolic conservation laws, SIAM J. Sci. Comput., 19 (1998), pp. 1892-1917.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 1892-1917
    • Jiang, G.-S.1    Tadmor, E.2
  • 10
    • 0034879339 scopus 로고    scopus 로고
    • A third-order semidiscrete central scheme for conservation laws and convection-diffusion equations
    • A. KURGANOV AND D. LEVY, A third-order semidiscrete central scheme for conservation laws and convection-diffusion equations, SIAM J. Sci. Comput., 22 (2000), pp. 1461-1488.
    • (2000) SIAM J. Sci. Comput. , vol.22 , pp. 461-1488
    • Kurganov, A.1    Levy, D.2
  • 11
    • 0036288577 scopus 로고    scopus 로고
    • Semidiscrete central-upwind schemes for hyperbolic conservation laws and Harnilton - Jacobi equations
    • A. KURGANOV, S. NOELLE, AND G. PETROVA, Semidiscrete central-upwind schemes for hyperbolic conservation laws and Harnilton - Jacobi equations, SIAM J. Sci. Comput., 23 (2001), pp. 707-740.
    • (2001) SIAM J. Sci. Comput. , vol.23 , pp. 707-740
    • Kurganov, A.1    Noelle, S.2    Petrova, G.3
  • 12
    • 0041025209 scopus 로고    scopus 로고
    • A third-order semi-discrete genuinely multidimensional central scheme for hyperbolic conservation laws and related problems
    • A. KURGANOV AND G. PETROVA, A third-order semi-discrete genuinely multidimensional central scheme for hyperbolic conservation laws and related problems, Numer. Math., 88 (2001), pp. 683-729.
    • (2001) Numer. Math. , vol.88 , pp. 683-729
    • Kurganov, A.1    Petrova, G.2
  • 13
    • 0347987814 scopus 로고    scopus 로고
    • New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
    • A. KURGANOV AND E. TADMOR, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations, J. Comput. Phys., 160 (2000), pp. 214-282.
    • (2000) J. Comput. Phys. , vol.160 , pp. 214-282
    • Kurganov, A.1    Tadmor, E.2
  • 14
    • 0004333256 scopus 로고    scopus 로고
    • Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers
    • to appear
    • A. KURGANOV AND E. TADMOR, Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers, Numer. Methods Partial Differential Equations, to appear.
    • Numer. Methods Partial Differential Equations
    • Kurganov, A.1    Tadmor, E.2
  • 15
    • 84980078953 scopus 로고
    • Weak solutions of non-linear hyperbolic equations and their numerical computation
    • P. D. LAX, Weak solutions of non-linear hyperbolic equations and their numerical computation, Comm. Pure Appl. Math., 7 (1954), pp. 159-193.
    • (1954) Comm. Pure Appl. Math. , vol.7 , pp. 159-193
    • Lax, P.D.1
  • 16
    • 0001528721 scopus 로고    scopus 로고
    • Solution of two-dimensional Riemann problems of gas dynamics by positive schemes
    • P. D. LAX AND X.-D. LIU, Solution of two-dimensional Riemann problems of gas dynamics by positive schemes, SIAM J. Sci. Comput., 19 (1998), pp. 319-340.
    • (1998) SIAM J. Sci. Comput. , vol.19 , pp. 319-340
    • Lax, P.D.1    Liu, X.-D.2
  • 17
    • 2442433925 scopus 로고
    • Towards the ultimate conservative difference scheme, V. A second-order sequel to Godunov's method
    • B. VAN LEER, Towards the ultimate conservative difference scheme, V. A second-order sequel to Godunov's method, J. Comput. Phys., 32 (1979), pp. 101-136.
    • (1979) J. Comput. Phys. , vol.32 , pp. 101-136
    • Van Leer, B.1
  • 18
    • 0000669778 scopus 로고    scopus 로고
    • A third-order 2D central scheme for conservation laws
    • INRIA, Roquencourt, France
    • D. LEVY, A third-order 2D central scheme for conservation laws, in Systémes Hyperboliques: Nouveaux Schémas et Nouvelles Applications, Vol. I, INRIA, Roquencourt, France, 1998, pp. 489-504.
    • (1998) Systémes Hyperboliques: Nouveaux Schémas et Nouvelles Applications , vol.1 , pp. 489-504
    • Levy, D.1
  • 19
    • 0033468934 scopus 로고    scopus 로고
    • Central WENO schemes for hyperbolic systems of conservation laws
    • D. LEVY, G. PUPPO, AND G. Russo, Central WENO schemes for hyperbolic systems of conservation laws, M2AN Math. Model. Numer. Anal., 33 (1999), pp. 547-571.
    • (1999) M2AN Math. Model. Numer. Anal. , vol.33 , pp. 547-571
    • Levy, D.1    Puppo, G.2    Russo, G.3
  • 20
    • 0034190398 scopus 로고    scopus 로고
    • On the behavior of the total variation in CWENO methods for conservation laws
    • D. LEVY, G. PUPPO, AND G. RUSSO, On the behavior of the total variation in CWENO methods for conservation laws, Appl. Numer. Math., 33 (2000), pp. 415-421.
    • (2000) Appl. Numer. Math. , vol.33 , pp. 415-421
    • Levy, D.1    Puppo, G.2    Russo, G.3
  • 21
    • 0034190356 scopus 로고    scopus 로고
    • A third order central WENO scheme for 2D conservation laws
    • D. LEVY, G. PUPPO, AND G. RUSSO, A third order central WENO scheme for 2D conservation laws, Appl. Numer. Math., 33 (2000), pp. 407-414.
    • (2000) Appl. Numer. Math. , vol.33 , pp. 407-414
    • Levy, D.1    Puppo, G.2    Russo, G.3
  • 22
    • 0035075926 scopus 로고    scopus 로고
    • Compact central WENO schemes for multidimensional conservation laws
    • D. LEVY, G. PUPPO, AND G. RUSSO, Compact central WENO schemes for multidimensional conservation laws, SIAM J. Sci. Comput., 22 (2000), pp. 656-672.
    • (2000) SIAM J. Sci. Comput. , vol.22 , pp. 656-672
    • Levy, D.1    Puppo, G.2    Russo, G.3
  • 24
    • 0034431558 scopus 로고    scopus 로고
    • Central schemes for balance laws of relaxation type
    • S. F. LIOTTA, V. ROMANO, AND G. RUSSO, Central schemes for balance laws of relaxation type, SIAM J. Numer. Anal., 38 (2000), pp. 1337-1356.
    • (2000) SIAM J. Numer. Anal. , vol.38 , pp. 1337-1356
    • Liotta, S.F.1    Romano, V.2    Russo, G.3
  • 25
    • 1542576022 scopus 로고    scopus 로고
    • Nonoscillatory high order accurate self-similar maximum principle satisfying shock capturing schemes I
    • X.-D LIU AND S. OSHER, Nonoscillatory high order accurate self-similar maximum principle satisfying shock capturing schemes I, SIAM J. Numer. Anal., 33 (1996), pp. 760-779.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 760-779
    • Liu, X.-D.1    Osher, S.2
  • 26
    • 0000592595 scopus 로고
    • Weighted essentially non-oscillatory schemes
    • X.-D. LIU, S. OSHER, AND T. CHAN, Weighted essentially non-oscillatory schemes, J. Comput. Phys., 115 (1994), pp. 200-212.
    • (1994) J. Comput. Phys. , vol.115 , pp. 200-212
    • Liu, X.-D.1    Osher, S.2    Chan, T.3
  • 27
    • 0032336616 scopus 로고    scopus 로고
    • Third order nonoscillatory central scheme for hyperbolic conservation laws
    • X.-D. LIU AND E. TADMOR, Third order nonoscillatory central scheme for hyperbolic conservation laws, Numer. Math., 79 (1998), pp. 397-425.
    • (1998) Numer. Math. , vol.79 , pp. 397-425
    • Liu, X.-D.1    Tadmor, E.2
  • 28
    • 28144455569 scopus 로고
    • Non-oscillatory central differencing for hyperbolic conservation laws
    • H. NESSYAHU AND E. TADMOR, Non-oscillatory central differencing for hyperbolic conservation laws, J. Comput. Phys., 87 (1990), pp. 408-463.
    • (1990) J. Comput. Phys. , vol.87 , pp. 408-463
    • Nessyahu, H.1    Tadmor, E.2
  • 29
    • 0034378480 scopus 로고    scopus 로고
    • Numerical solution for hydrodynamical models of semiconductors
    • V. ROMANO AND G. Russo, Numerical solution for hydrodynamical models of semiconductors, Math. Models Methods Appl. Sci., 10 (2000), pp. 1099-1120.
    • (2000) Math. Models Methods Appl. Sci. , vol.10 , pp. 1099-1120
    • Romano, V.1    Russo, G.2
  • 30
    • 0001540763 scopus 로고
    • A high resolution staggered mesh approach for nonlinear hyperbolic systems of conservation laws
    • R. SANDERS AND A. WEISER, A high resolution staggered mesh approach for nonlinear hyperbolic systems of conservation laws, J. Comput. Phys., 101 (1992), pp. 314-329.
    • (1992) J. Comput. Phys. , vol.101 , pp. 314-329
    • Sanders, R.1    Weiser, A.2
  • 31
    • 0000034725 scopus 로고    scopus 로고
    • Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws
    • Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, A. Quarteroni, ed., Springer, Berlin
    • C.-W. SHU, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, in Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, Lecture Notes in Math. 1697, A. Quarteroni, ed., Springer, Berlin, 1998, pp. 325-432.
    • (1998) Lecture Notes in Math. , vol.1697 , pp. 325-432
    • Shu, C.-W.1
  • 32
    • 0001568854 scopus 로고
    • Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
    • C.-W. SHU AND S. OSHER, Efficient implementation of essentially non-oscillatory shock-capturing schemes, II, J. Comput. Phys., 83 (1989), pp. 32-78.
    • (1989) J. Comput. Phys. , vol.83 , pp. 32-78
    • Shu, C.-W.1    Osher, S.2
  • 33
    • 0346863656 scopus 로고
    • Classification of the Riemann problem for two-dimensional gas dynamics
    • C. W. SCHULZ-RINNE, Classification of the Riemann problem for two-dimensional gas dynamics, SIAM J. Math. Anal., 24 (1993), pp. 76-88.
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 76-88
    • Schulz-Rinne, C.W.1
  • 34
    • 0003332686 scopus 로고
    • Numerical solution of the Riemann problem for two-dimensional gas dynamics
    • C. W. SCHULZ-RINNE, J. P. COLLINS, AND H. M. GLAZ, Numerical solution of the Riemann problem for two-dimensional gas dynamics, SIAM J. Sci. Comput., 14 (1993), pp. 1394-1414.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 1394-1414
    • Schulz-Rinne, C.W.1    Collins, J.P.2    Glaz, H.M.3
  • 35
    • 2942705023 scopus 로고
    • A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
    • G. SOD, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, J. Comput. Phys., 22 (1978), pp. 1-31.
    • (1978) J. Comput. Phys. , vol.22 , pp. 1-31
    • Sod, G.1
  • 37
    • 0002033981 scopus 로고    scopus 로고
    • Approximate solutions of nonlinear conservation laws
    • Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, A. Quarteroni, ed., Springer, Berlin
    • E. TADMOR, Approximate solutions of nonlinear conservation laws, in Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, Lecture Notes in Math. 1697, A. Quarteroni, ed., Springer, Berlin, 1998, pp. 1-149.
    • (1998) Lecture Notes in Math. , vol.1697 , pp. 1-149
    • Tadmor, E.1
  • 38
    • 48749139407 scopus 로고
    • The numerical simulation of two-dimensional fluid flow with strong shocks
    • P. WOODWARD AND P. COLELLA, The numerical simulation of two-dimensional fluid flow with strong shocks, J. Comput. Phys., 54 (1984), pp. 115-173.
    • (1984) J. Comput. Phys. , vol.54 , pp. 115-173
    • Woodward, P.1    Colella, P.2
  • 39
    • 84966233444 scopus 로고
    • Natural continuous extensions of Runge-Kutta methods
    • M. ZENNARO, Natural continuous extensions of Runge-Kutta methods, Math. Comp., 46 (1986), pp. 119-133.
    • (1986) Math. Comp. , vol.46 , pp. 119-133
    • Zennaro, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.