메뉴 건너뛰기




Volumn 32, Issue 6, 2009, Pages 834-844

Well-balanced high-order centred schemes for non-conservative hyperbolic systems. Applications to shallow water equations with fixed and mobile bed

Author keywords

ADER; Centred schemes; FORCE; High order WENO finite volume methods; Non conservative hyperbolic systems; Sediment transport; Shallow water equations

Indexed keywords

ADER; CENTRED SCHEMES; FORCE; HIGH-ORDER WENO FINITE VOLUME METHODS; NON-CONSERVATIVE HYPERBOLIC SYSTEMS; SHALLOW WATER EQUATIONS;

EID: 67349107188     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2009.02.006     Document Type: Article
Times cited : (133)

References (34)
  • 1
    • 44049097379 scopus 로고    scopus 로고
    • Morphological evolution of steep-sloped river beds in the presence of a hydraulic jump. In: Experimental study
    • paper presented at
    • Bellal M, Spinewine C, Zech Y. Morphological evolution of steep-sloped river beds in the presence of a hydraulic jump. In: Experimental study, paper presented at XXX IAHR congress, 2003. p. 133-40.
    • (2003) XXX IAHR congress , pp. 133-140
    • Bellal, M.1    Spinewine, C.2    Zech, Y.3
  • 2
    • 0028534347 scopus 로고
    • Upwind methods for hyperbolic conservation-laws with source terms
    • Bermudez A., and Vazquez E. Upwind methods for hyperbolic conservation-laws with source terms. Comput Fluids 23 8 (1994) 1049-1071
    • (1994) Comput Fluids , vol.23 , Issue.8 , pp. 1049-1071
    • Bermudez, A.1    Vazquez, E.2
  • 3
    • 33847010906 scopus 로고    scopus 로고
    • High-order balanced cweno scheme for movable bed shallow water equations
    • Caleffi V., and Valiani A. High-order balanced cweno scheme for movable bed shallow water equations. Adv Water Resour 30 (2007) 730-741
    • (2007) Adv Water Resour , vol.30 , pp. 730-741
    • Caleffi, V.1    Valiani, A.2
  • 4
    • 37349007276 scopus 로고    scopus 로고
    • Sediment transport models in shallow water equations and numerical approach by high order finite volume methods
    • Castro M., Ferndandez-Nieto E.D., and Ferreiro A. Sediment transport models in shallow water equations and numerical approach by high order finite volume methods. Comput Fluids 37 3 (2008) 299-316
    • (2008) Comput Fluids , vol.37 , Issue.3 , pp. 299-316
    • Castro, M.1    Ferndandez-Nieto, E.D.2    Ferreiro, A.3
  • 5
    • 33746371365 scopus 로고    scopus 로고
    • High-order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products applications to shallow-water systems
    • Castro M., Gallardo J., and Parés C. High-order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products applications to shallow-water systems. Math Comput 75 (2006) 1103-1134
    • (2006) Math Comput , vol.75 , pp. 1103-1134
    • Castro, M.1    Gallardo, J.2    Parés, C.3
  • 6
    • 47049112379 scopus 로고    scopus 로고
    • Why many theories of shock waves are necessary: convergence error in formally path-consistent schemes
    • Castro M., LeFloch P., Muñoz M.L., and Parés C. Why many theories of shock waves are necessary: convergence error in formally path-consistent schemes. J Comput Phys 227 (2008) 8107-8129
    • (2008) J Comput Phys , vol.227 , pp. 8107-8129
    • Castro, M.1    LeFloch, P.2    Muñoz, M.L.3    Parés, C.4
  • 7
    • 62949191303 scopus 로고    scopus 로고
    • Coefficient-splitting numerical schemes for nonconservative hyperbolic systems and high order extensions
    • submitted for publication
    • Castro M, Pardo A, Parés C, Toro E. Coefficient-splitting numerical schemes for nonconservative hyperbolic systems and high order extensions, submitted for publication.
    • Castro, M.1    Pardo, A.2    Parés, C.3    Toro, E.4
  • 8
    • 13644283237 scopus 로고    scopus 로고
    • Centered difference schemes for nonlinear hyperbolic equations
    • Chen G., and Toro E. Centered difference schemes for nonlinear hyperbolic equations. J Hyperbolic Diff Eq 1 3 (2004) 531-566
    • (2004) J Hyperbolic Diff Eq , vol.1 , Issue.3 , pp. 531-566
    • Chen, G.1    Toro, E.2
  • 9
    • 0001522672 scopus 로고
    • Definition and weak stability of nonconservative products
    • DalMaso G., LeFloch P., and Murat F. Definition and weak stability of nonconservative products. J Math Pure Appl 74 6 (1995) 483-548
    • (1995) J Math Pure Appl , vol.74 , Issue.6 , pp. 483-548
    • DalMaso, G.1    LeFloch, P.2    Murat, F.3
  • 10
    • 48149096340 scopus 로고    scopus 로고
    • A unified framework for the construction of one-step finite-volume and discontinuous Galerkin schemes
    • Dumbser M., Balsara D., Toro E., and Munz C. A unified framework for the construction of one-step finite-volume and discontinuous Galerkin schemes. J Comput Phys 227 (2008) 8209-8253
    • (2008) J Comput Phys , vol.227 , pp. 8209-8253
    • Dumbser, M.1    Balsara, D.2    Toro, E.3    Munz, C.4
  • 11
    • 40249111500 scopus 로고    scopus 로고
    • Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws
    • Dumbser M., Enaux C., and Toro E. Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws. J Comput Phys 227 (2008) 3971-4001
    • (2008) J Comput Phys , vol.227 , pp. 3971-4001
    • Dumbser, M.1    Enaux, C.2    Toro, E.3
  • 12
    • 33846336138 scopus 로고    scopus 로고
    • Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems
    • Dumbser M., and Käser M. Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems. J Comput Phys 221 (2007) 693-723
    • (2007) J Comput Phys , vol.221 , pp. 693-723
    • Dumbser, M.1    Käser, M.2
  • 13
    • 34548397128 scopus 로고    scopus 로고
    • Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems
    • Dumbser M., Käser M., Titarev V., and Toro E. Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems. J Comput Phys 226 (2007) 204-243
    • (2007) J Comput Phys , vol.226 , pp. 204-243
    • Dumbser, M.1    Käser, M.2    Titarev, V.3    Toro, E.4
  • 14
    • 33745038766 scopus 로고    scopus 로고
    • Building blocks for arbitrary high order discontinuous Galerkin schemes
    • Dumbser M., and Munz C. Building blocks for arbitrary high order discontinuous Galerkin schemes. J Sci Comput 27 (2006) 215-230
    • (2006) J Sci Comput , vol.27 , pp. 215-230
    • Dumbser, M.1    Munz, C.2
  • 15
    • 84981759861 scopus 로고
    • Solution in the large for nonlinear hyperbolic systems of equations
    • Glimm J. Solution in the large for nonlinear hyperbolic systems of equations. Commun Pure Appl Math 18 (1965) 697-715
    • (1965) Commun Pure Appl Math , vol.18 , pp. 697-715
    • Glimm, J.1
  • 16
    • 0034209981 scopus 로고    scopus 로고
    • A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms
    • Gosse L. A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms. Comput Math Appl 39 9-10 (2000) 135-159
    • (2000) Comput Math Appl , vol.39 , Issue.9-10 , pp. 135-159
    • Gosse, L.1
  • 17
    • 0035590547 scopus 로고    scopus 로고
    • A well-balanced scheme using non-conservative products designed for hyperbolic systems of conservation laws with source terms
    • Gosse L. A well-balanced scheme using non-conservative products designed for hyperbolic systems of conservation laws with source terms. Math Models Methods Appl Sci 11 2 (2001) 339-365
    • (2001) Math Models Methods Appl Sci , vol.11 , Issue.2 , pp. 339-365
    • Gosse, L.1
  • 18
    • 67349174266 scopus 로고    scopus 로고
    • Goutal N, Maurel F. In: Proceedings of the second workshop on dam-breakwave simulation. Technical Report HE-43/97/016/A, Electricité de France, Département Laboratoire National d'Hydraulique, Groupe Hydraulique Fluviale, 1997.
    • Goutal N, Maurel F. In: Proceedings of the second workshop on dam-breakwave simulation. Technical Report HE-43/97/016/A, Electricité de France, Département Laboratoire National d'Hydraulique, Groupe Hydraulique Fluviale, 1997.
  • 19
    • 33749725182 scopus 로고
    • Uniformly high order essentially non-oscillatory schemes III
    • Harten A., Engquist B., Osher S., and Chakravarthy S. Uniformly high order essentially non-oscillatory schemes III. 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    Chakravarthy, S.4
  • 20
    • 84968497746 scopus 로고
    • Why non-conservative schemes converge to the wrong solutions: error analysis
    • Hou T., and LeFloch P. Why non-conservative schemes converge to the wrong solutions: error analysis. Math Comput 62 (1994) 497-530
    • (1994) Math Comput , vol.62 , pp. 497-530
    • Hou, T.1    LeFloch, P.2
  • 21
    • 0030161771 scopus 로고    scopus 로고
    • Efficient implementation of weighted ENO schemes
    • Jiang G., and Shu C. Efficient implementation of weighted ENO schemes. J Comput Phys 126 (1996) 202-228
    • (1996) J Comput Phys , vol.126 , pp. 202-228
    • Jiang, G.1    Shu, C.2
  • 22
    • 0001315315 scopus 로고    scopus 로고
    • Balancing source terms and flux gradients in high-resolution Godunov methods: the quasi-steady wave-propagation algorithm
    • LeVeque R. Balancing source terms and flux gradients in high-resolution Godunov methods: the quasi-steady wave-propagation algorithm. J Comput Phys 146 1 (1998) 346-365
    • (1998) J Comput Phys , vol.146 , Issue.1 , pp. 346-365
    • LeVeque, R.1
  • 23
    • 0000592595 scopus 로고
    • Weighted essentially non-oscillatory schemes
    • Liu X., Osher S., and Chan T. Weighted essentially non-oscillatory schemes. J Comput Phys 115 (1994) 200-212
    • (1994) J Comput Phys , vol.115 , pp. 200-212
    • Liu, X.1    Osher, S.2    Chan, T.3
  • 24
    • 0036610752 scopus 로고    scopus 로고
    • St. Venant Exner equations for near-critical transcritical flows
    • Lyn D., and Altinakar M. St. Venant Exner equations for near-critical transcritical flows. J Hydraul Eng, ASCE 128 6 (2002) 579-587
    • (2002) J Hydraul Eng, ASCE , vol.128 , Issue.6 , pp. 579-587
    • Lyn, D.1    Altinakar, M.2
  • 25
    • 67349214676 scopus 로고    scopus 로고
    • Meyer-Peter E, Müller R, Formulas for bed-load transport. In: Report on 2nd meeting on international association on hydraulic structures research, Stockholm, 1948. p. 39-64.
    • Meyer-Peter E, Müller R, Formulas for bed-load transport. In: Report on 2nd meeting on international association on hydraulic structures research, Stockholm, 1948. p. 39-64.
  • 26
    • 33847668045 scopus 로고    scopus 로고
    • Numerical methods for nonconservative hyperbolic systems: a theoretical framework
    • Parés C. Numerical methods for nonconservative hyperbolic systems: a theoretical framework. SIAM J Numer Anal 44 (2006) 300-321
    • (2006) SIAM J Numer Anal , vol.44 , pp. 300-321
    • Parés, C.1
  • 27
    • 0025572047 scopus 로고
    • Surface-based bedload transport relation for gravel rivers
    • Parker G. Surface-based bedload transport relation for gravel rivers. J Hydraul Res 28 4 (1990) 417-436
    • (1990) J Hydraul Res , vol.28 , Issue.4 , pp. 417-436
    • Parker, G.1
  • 28
    • 52649106483 scopus 로고    scopus 로고
    • Quasi-conservative formulation of the one dimensional Saint Venant-Exner model
    • Siviglia A., Nobile G., and Colombini M. Quasi-conservative formulation of the one dimensional Saint Venant-Exner model. J Hydraul Eng 134 10 (2008) 1521-1526
    • (2008) J Hydraul Eng , vol.134 , Issue.10 , pp. 1521-1526
    • Siviglia, A.1    Nobile, G.2    Colombini, M.3
  • 29
    • 0041819638 scopus 로고    scopus 로고
    • PRICE: primitive centred schemes for hyperbolic system of equations
    • Toro E., and Siviglia A. PRICE: primitive centred schemes for hyperbolic system of equations. Int J Numer Methods Fluids 42 (2003) 1263-1291
    • (2003) Int J Numer Methods Fluids , vol.42 , pp. 1263-1291
    • Toro, E.1    Siviglia, A.2
  • 30
    • 57249099681 scopus 로고    scopus 로고
    • Solution of the generalized Riemann problem for advection-reaction equations
    • Toro E., and Titarev V. Solution of the generalized Riemann problem for advection-reaction equations. Proc Roy Soc Lond Ser A - Math Phys Eng Sci 458 2018 (2002) 271-281
    • (2002) Proc Roy Soc Lond Ser A - Math Phys Eng Sci , vol.458 , Issue.2018 , pp. 271-281
    • Toro, E.1    Titarev, V.2
  • 31
    • 0002376210 scopus 로고    scopus 로고
    • On Glimm-Related Schemes for Conservation Laws
    • Technical Report MMU-9602, Department of Mathematics and Physics, Manchester Metropolitan University, UK
    • Toro EF. On Glimm-Related Schemes for Conservation Laws. Technical Report MMU-9602, Department of Mathematics and Physics, Manchester Metropolitan University, UK, 1996.
    • (1996)
    • Toro, E.F.1
  • 32
    • 0033634093 scopus 로고    scopus 로고
    • Centred TVD schemes for hyperbolic conservation laws
    • Toro E.F., and Billett S.J. Centred TVD schemes for hyperbolic conservation laws. IMA J Numer Anal 20 (2000) 47-79
    • (2000) IMA J Numer Anal , vol.20 , pp. 47-79
    • Toro, E.F.1    Billett, S.J.2
  • 33
    • 0001124468 scopus 로고
    • A weak formulation of Roe's approximate riemann solver
    • Toumi I. A weak formulation of Roe's approximate riemann solver. J Comput Phys 102 2 (1992) 360-373
    • (1992) J Comput Phys , vol.102 , Issue.2 , pp. 360-373
    • Toumi, I.1
  • 34
    • 33745036537 scopus 로고    scopus 로고
    • High-order well-balanced finite difference WENO schemes for a class of hyperbolic systems with source terms
    • Xing Y., and Shu C. High-order well-balanced finite difference WENO schemes for a class of hyperbolic systems with source terms. J Sci Comput 27 1-3 (2006) 477-494
    • (2006) J Sci Comput , vol.27 , Issue.1-3 , pp. 477-494
    • Xing, Y.1    Shu, C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.