메뉴 건너뛰기




Volumn 26, Issue 6, 2010, Pages 1675-1692

A fourth-order central runge-kutta scheme for hyperbolic conservation laws

Author keywords

Central Runge Kutta(CRK) scheme; Central scheme; Hyperbolic conservation laws; Nonlinear limiters; Nonoscillatory scheme; Weighted essentially nonoscillatory (WENO) technique

Indexed keywords

CENTRAL SCHEME; HYPERBOLIC CONSERVATION LAWS; NONLINEAR LIMITERS; NONOSCILLATORY; RUNGE-KUTTA; WEIGHTED ESSENTIALLY NONOSCILLATORY;

EID: 78650086755     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20530     Document Type: Article
Times cited : (12)

References (29)
  • 1
    • 34447253569 scopus 로고    scopus 로고
    • Nonmonotone chemotactic invasion: High-resolution simulation, phase plane analysis and new benchmark problems
    • M. Simpson and K. Landman, Nonmonotone chemotactic invasion: high-resolution simulation, phase plane analysis and new benchmark problems, J Comput Phys 225 (2007), 6-12.
    • (2007) J Comput Phys , vol.225 , pp. 6-12
    • Simpson, M.1    Landman, K.2
  • 3
    • 0034386606 scopus 로고    scopus 로고
    • Central schemes for hydrodynamical limits of discrete-velocity kinetic models
    • E. Gabetta, L. Pareschi, and M. Ronconi, Central schemes for hydrodynamical limits of discrete-velocity kinetic models, Trans Theo Stat Phys 29 (2000), 465-477.
    • (2000) Trans Theo Stat Phys , vol.29 , pp. 465-477
    • Gabetta, E.1    Pareschi, L.2    Ronconi, M.3
  • 4
    • 33847750208 scopus 로고    scopus 로고
    • Non-oscillatory central schemes for one-and two-dimensionalMHDequations. II: High-order semi-discrete schemes
    • J. Balbas and E. Tadmor, Non-oscillatory central schemes for one-and two-dimensionalMHDequations. II: High-order semi-discrete schemes, SIAM J Sci Comput 28 (2006), 533-560.
    • (2006) SIAM J Sci Comput , vol.28 , pp. 533-560
    • Balbas, J.1    Tadmor, E.2
  • 5
    • 32644435892 scopus 로고    scopus 로고
    • Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices
    • M. Dehghan, Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices, Mathematics Comput Simul 71 (2006), 16-30.
    • (2006) Mathematics Comput Simul , vol.71 , pp. 16-30
    • Dehghan, M.1
  • 6
    • 11144275388 scopus 로고    scopus 로고
    • On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation
    • M. Dehghan, On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation, Numer Methods Partial Differential Eq 21 (2005), 24-40.
    • (2005) Numer Methods Partial Differential Eq , vol.21 , pp. 24-40
    • Dehghan, M.1
  • 7
    • 0003733595 scopus 로고    scopus 로고
    • Finite volume methods for hyperbolic problems
    • Cambridge University Press, Cambridge, UK
    • R. J. LeVeque, Finite volume methods for hyperbolic problems, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, UK, 2002.
    • (2002) Cambridge Texts in Applied Mathematics
    • LeVeque, R.J.1
  • 8
    • 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), 379-425.
    • (1998) Numer Math , vol.79 , pp. 379-425
    • Liu, X.D.1    Tadmor, E.2
  • 9
    • 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), 408-463.
    • (1990) J Comput Phys , vol.87 , pp. 408-463
    • Nessyahu, H.1    Tadmor, E.2
  • 10
    • 41149117153 scopus 로고    scopus 로고
    • A new fourth-order non-oscillatory central scheme for hyperbolic conservation laws
    • A. A. I. Peer, A. Gopaul, M. Z. Dauhoo, and M. Bhuruth, A new fourth-order non-oscillatory central scheme for hyperbolic conservation laws, Appl Numer Math 58 (2008), 674-688.
    • (2008) Appl Numer Math , vol.58 , pp. 674-688
    • Peer, A.A.I.1    Gopaul, A.2    Dauhoo, M.Z.3    Bhuruth, M.4
  • 11
    • 0000935266 scopus 로고
    • A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics
    • S. K. Godunov, A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics, Math Sb 47 (1959), 271-290.
    • (1959) Math Sb , vol.47 , pp. 271-290
    • Godunov, S.K.1
  • 12
    • 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 68 (1971), 1686-1688.
    • (1971) Proc Nat Acad Sci , vol.68 , pp. 1686-1688
    • Friedrichs, K.O.1    Lax, P.D.2
  • 13
    • 0032206542 scopus 로고    scopus 로고
    • Nonoscillatory central schemes for multidimensional hyperbolic conservation laws
    • PII S106482759631041X
    • G. S. Jiang and E. Tadmor, Nonoscillatory central schemes for multidimensional hyperbolic conservation laws, SIAM J Sci Comput 19 (1998), 1892-1917. (Pubitemid 128614424)
    • (1998) SIAM Journal of Scientific Computing , vol.19 , Issue.6 , pp. 1892-1917
    • Jiang, G.-S.1    Tadmor, E.2
  • 14
    • 1542576022 scopus 로고    scopus 로고
    • Non-oscillatory high order accurate self-similar maximum principle satisfying shock capturing schemes I
    • X. D. Liu and S. Osher, Non-oscillatory high order accurate self-similar maximum principle satisfying shock capturing schemes I, SIAM J Numer Anal 33 (1996), 760-779.
    • (1996) SIAM J Numer Anal , vol.33 , pp. 760-779
    • Liu, X.D.1    Osher, S.2
  • 15
    • 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), 1099-1120.
    • (2000) Math Models Methods Appl Sci , vol.10 , pp. 1099-1120
    • Romano, V.1    Russo, G.2
  • 16
    • 0035453003 scopus 로고    scopus 로고
    • Central differencing based numerical schemes for hyperbolic conservation laws with relaxation terms
    • L. Pareschi, Central differencing based numerical schemes for hyperbolic conservation laws with relaxation terms, SIAM J Numer Anal 39 (2001), 1395-1417.
    • (2001) SIAM J Numer Anal , vol.39 , pp. 1395-1417
    • Pareschi, L.1
  • 17
    • 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), 1337-1356.
    • (2000) SIAM J Numer Anal , vol.38 , pp. 1337-1356
    • Liotta, S.F.1    Romano, V.2    Russo, G.3
  • 18
    • 0038792198 scopus 로고    scopus 로고
    • High-order semi-discrete central-upwind schemes for multi-dimensional Hamilton-Jacobi equations
    • S. Bryson and D. Levy, High-order semi-discrete central-upwind schemes for multi-dimensional Hamilton-Jacobi equations, J Comput Phys 189 (2003), 63-87.
    • (2003) J Comput Phys , vol.189 , pp. 63-87
    • Bryson, S.1    Levy, D.2
  • 19
    • 19644362553 scopus 로고    scopus 로고
    • Central Runge Kutta schemes for conservation laws
    • L. Pareschi, G. Puppo, and G. Russo, Central Runge Kutta schemes for conservation laws, SIAM J Sci Comput 26 (2005), 979-999.
    • (2005) SIAM J Sci Comput , vol.26 , pp. 979-999
    • Pareschi, L.1    Puppo, G.2    Russo, G.3
  • 20
    • 84966233444 scopus 로고
    • Natural continuous extensions of Runge-Kutta methods
    • M. Zennaro, Natural continuous extensions of Runge-Kutta methods, Math Comp 46 (1986), 119-133.
    • (1986) Math Comp , vol.46 , pp. 119-133
    • Zennaro, M.1
  • 21
    • 0036288577 scopus 로고    scopus 로고
    • Semi-discrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations
    • A. Kurganov, S. Noelle, and G. Petrova, Semi-discrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations, SIAM J Sci Comput 23 (2001), 707-740.
    • (2001) SIAM J Sci Comput , vol.23 , pp. 707-740
    • Kurganov, A.1    Noelle, S.2    Petrova, G.3
  • 22
    • 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), 294-322.
    • (1999) SIAM J Sci Comput , vol.21 , pp. 294-322
    • Bianco, F.1    Puppo, G.2    Russo, G.3
  • 23
    • 0023329384 scopus 로고
    • Uniformly high-order accurate nonoscillatory schemes, I
    • A. Harten and S. Osher, 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
  • 25
    • 69249239096 scopus 로고    scopus 로고
    • Finite difference schemes and partial differential equations
    • J. C. Strikwerda, Finite difference schemes and partial differential equations, SIAM, 2004.
    • (2004) SIAM
    • Strikwerda, J.C.1
  • 26
    • 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 semidiscrete genuinely multidimensional central scheme for hyperbolic conservation laws and related problems, Numer Math 88 (2001), 683-729. (Pubitemid 33580693)
    • (2001) Numerische Mathematik , vol.88 , Issue.4 , pp. 683-729
    • Kurganov, A.1    Petrova, G.2
  • 27
    • 0347987814 scopus 로고    scopus 로고
    • New high-resolution central schemes for non-linear conservation laws and convection-diffusion equations
    • A. Kurganov and E. Tadmor, New high-resolution central schemes for non-linear conservation laws and convection-diffusion equations, J Comput Phys 160 (2000), 241-282.
    • (2000) J Comput Phys , vol.160 , pp. 241-282
    • Kurganov, A.1    Tadmor, E.2
  • 28
    • 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, Math Model Numer Anal 33 (1999), 547-571.
    • (1999) Math Model Numer Anal , vol.33 , pp. 547-571
    • Levy, D.1    Puppo, G.2    Russo, G.3
  • 29
    • 0037249089 scopus 로고    scopus 로고
    • A fourth-order central WENO schemes for multidimensional hyperbolic systems of conservation laws
    • D. Levy, G. Puppo, and G. Russo, A fourth-order central WENO schemes for multidimensional hyperbolic systems of conservation laws, SIAM J Sci Comput 24 (2002), 456-480.
    • (2002) SIAM J Sci Comput , vol.24 , pp. 456-480
    • Levy, D.1    Puppo, G.2    Russo, G.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.