메뉴 건너뛰기




Volumn 226, Issue 1, 2007, Pages 180-203

Well-balanced finite volume schemes for pollutant transport by shallow water equations on unstructured meshes

Author keywords

Finite volume method; Pollutant transport; Shallow water equations; Strait of Gibraltar; Unstructured grids

Indexed keywords

EQUATIONS OF MOTION; FLOW OF WATER; HYDRAULICS; NUMERICAL METHODS; WATER POLLUTION;

EID: 34548509905     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.04.005     Document Type: Article
Times cited : (116)

References (41)
  • 1
    • 0037405142 scopus 로고    scopus 로고
    • Efficient numerical approximation of compressible multi-material flow for unstructured meshes
    • Abgrall R., Nkonga B., and Saurel R. Efficient numerical approximation of compressible multi-material flow for unstructured meshes. Comput. Fluids 32 4 (2003) 571-605
    • (2003) Comput. Fluids , vol.32 , Issue.4 , pp. 571-605
    • Abgrall, R.1    Nkonga, B.2    Saurel, R.3
  • 2
    • 0035399697 scopus 로고    scopus 로고
    • Time-line cubic spline interpolation scheme for solution of advection equation
    • Ahmad Z., and Kothyari U.C. Time-line cubic spline interpolation scheme for solution of advection equation. Comput. Fluids. 30 (2001) 737-752
    • (2001) Comput. Fluids. , vol.30 , pp. 737-752
    • Ahmad, Z.1    Kothyari, U.C.2
  • 3
    • 0023728045 scopus 로고
    • Models for flood propagation on initially dry land
    • Akanbi A.A., and Katopodes N.D. Models for flood propagation on initially dry land. J. Hydraul. Eng. (ASCE). 114 (1988) 686-695
    • (1988) J. Hydraul. Eng. (ASCE). , vol.114 , pp. 686-695
    • Akanbi, A.A.1    Katopodes, N.D.2
  • 4
    • 0035399783 scopus 로고    scopus 로고
    • Exact solutions to the Riemann problem of the shallow water equations with a bottom step
    • Alcrudo F., and Benkhaldoun F. Exact solutions to the Riemann problem of the shallow water equations with a bottom step. Comput. Fluids. 30 (2001) 643-671
    • (2001) Comput. Fluids. , vol.30 , pp. 643-671
    • Alcrudo, F.1    Benkhaldoun, F.2
  • 5
    • 0027561554 scopus 로고
    • A high resolution Godunov-type scheme in finite volumes for the 2D shallow water equation
    • Alcrudo F., and Garcia-Navarro P. A high resolution Godunov-type scheme in finite volumes for the 2D shallow water equation. Int. J. Numer. Meth. Fluids 16 (1993) 489-505
    • (1993) Int. J. Numer. Meth. Fluids , vol.16 , pp. 489-505
    • Alcrudo, F.1    Garcia-Navarro, P.2
  • 6
    • 85190152164 scopus 로고    scopus 로고
    • J.I. Almazán, H. Bryden, T. Kinder, G. Parrilla, (Eds.), Seminario Sobre la Oceanografi{dotless}́a Fi{dotless}́sica del Estrecho de Gibraltar, SECEG, Madrid, 1988.
  • 7
    • 4644342716 scopus 로고    scopus 로고
    • A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows
    • Audusse E., Bouchut F., Bristeau M.O., Klein R., and Perthame B. A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comp. 25 (2004) 2050-2065
    • (2004) SIAM J. Sci. Comp. , vol.25 , pp. 2050-2065
    • Audusse, E.1    Bouchut, F.2    Bristeau, M.O.3    Klein, R.4    Perthame, B.5
  • 8
    • 0029504921 scopus 로고
    • A posteriori estimation and adaptive control of the pollution error in the h-version of finte-element method
    • Babuska I., Strouboulis T., Updhyay C.S., and Gangaraj S.K. A posteriori estimation and adaptive control of the pollution error in the h-version of finte-element method. Int. J. Numer. Meth. Eng. 38 (1995) 4207-4235
    • (1995) Int. J. Numer. Meth. Eng. , vol.38 , pp. 4207-4235
    • Babuska, I.1    Strouboulis, T.2    Updhyay, C.S.3    Gangaraj, S.K.4
  • 9
    • 33749003980 scopus 로고    scopus 로고
    • A non homogeous Riemann solver for shallow water and two phase flows
    • Benkhaldoun F., and Quivy L. A non homogeous Riemann solver for shallow water and two phase flows. Flow Turbul. Combust. 76 (2006) 391-402
    • (2006) Flow Turbul. Combust. , vol.76 , pp. 391-402
    • Benkhaldoun, F.1    Quivy, L.2
  • 10
    • 26144438389 scopus 로고    scopus 로고
    • Analysis and validation of a new finite volume scheme for nonhomogeneous systems
    • Herbin R., and Kroner D. (Eds), Hermes Science Publications
    • Benkhaldoun F. Analysis and validation of a new finite volume scheme for nonhomogeneous systems. In: Herbin R., and Kroner D. (Eds). Finite Volumes for Complex Applications IV: Problems & Perspectives (2002), Hermes Science Publications 269-276
    • (2002) Finite Volumes for Complex Applications IV: Problems & Perspectives , pp. 269-276
    • Benkhaldoun, F.1
  • 11
    • 0028534347 scopus 로고
    • Upwind methods for hyperbolic conservation laws with source terms
    • Bermúdez A., and Vázquez M.E. Upwind methods for hyperbolic conservation laws with source terms. Comput. Fluids 23 (1994) 1049-1071
    • (1994) Comput. Fluids , vol.23 , pp. 1049-1071
    • Bermúdez, A.1    Vázquez, M.E.2
  • 12
    • 11144271526 scopus 로고    scopus 로고
    • Ignition of fuel issuing from a porous cylinder located adjacent to a heated wall: a numerical study
    • Elmahi I., Benkhaldoun F., Borghi R., and Raghay S. Ignition of fuel issuing from a porous cylinder located adjacent to a heated wall: a numerical study. Combust. Theory Modell. 8 (2004) 789-809
    • (2004) Combust. Theory Modell. , vol.8 , pp. 789-809
    • Elmahi, I.1    Benkhaldoun, F.2    Borghi, R.3    Raghay, S.4
  • 13
    • 1542576141 scopus 로고    scopus 로고
    • A well balanced scheme for the numerical processing of source terms in hyperbolic equation
    • Greenberg J.M., and Le Roux A.Y. A well balanced scheme for the numerical processing of source terms in hyperbolic equation. SIAM J. Numer. Anal. 33 (1996) 1-16
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1-16
    • Greenberg, J.M.1    Le Roux, A.Y.2
  • 14
    • 0037716742 scopus 로고    scopus 로고
    • The role of the exchanges through the Starit of Gibraltar on the budget of elements in Western Mediterranean Sea: consequences of humain-induced modifications
    • Gómez F. The role of the exchanges through the Starit of Gibraltar on the budget of elements in Western Mediterranean Sea: consequences of humain-induced modifications. Marine Pollut. Bull. 46 (2003) 685-694
    • (2003) Marine Pollut. Bull. , vol.46 , pp. 685-694
    • Gómez, F.1
  • 15
    • 34548497221 scopus 로고    scopus 로고
    • Finite element modified method of characteristics for shallow water flows: application to the Strait of Gibraltar
    • González M., and Seaïd M. Finite element modified method of characteristics for shallow water flows: application to the Strait of Gibraltar. Prog. Indust. Math. 8 (2005) 518-522
    • (2005) Prog. Indust. Math. , vol.8 , pp. 518-522
    • González, M.1    Seaïd, M.2
  • 17
    • 0034635198 scopus 로고    scopus 로고
    • A two-dimensional finite element drying-wetting shallow water model for rivers and estuaries
    • Heniche M., Secretan Y., Boudreau P., and Leclerc M. A two-dimensional finite element drying-wetting shallow water model for rivers and estuaries. Adv. Water Resour. 23 (2000) 359-372
    • (2000) Adv. Water Resour. , vol.23 , pp. 359-372
    • Heniche, M.1    Secretan, Y.2    Boudreau, P.3    Leclerc, M.4
  • 18
    • 85190160429 scopus 로고    scopus 로고
    • F. Hermeline, Une méthode automatique de maillage en dimension n, PhD Thesis, Université de Paris 6, 1980.
  • 19
    • 0034177347 scopus 로고    scopus 로고
    • Development of Physically Based Neshes for Two-Dimensional Models of Meandering Channel flow
    • Horrit M.S. Development of Physically Based Neshes for Two-Dimensional Models of Meandering Channel flow. Int. J. Numer. Methods Eng. 47 (2000) 2019-2037
    • (2000) Int. J. Numer. Methods Eng. , vol.47 , pp. 2019-2037
    • Horrit, M.S.1
  • 20
    • 0030925925 scopus 로고    scopus 로고
    • Refined numerical scheme for advective transport in diffusion simulation
    • Komatsu T., Ohgushi K., and Asai K. Refined numerical scheme for advective transport in diffusion simulation. J. Hydraulic Eng. 123 (1997) 41-50
    • (1997) J. Hydraulic Eng. , vol.123 , pp. 41-50
    • Komatsu, T.1    Ohgushi, K.2    Asai, K.3
  • 21
    • 0036333838 scopus 로고    scopus 로고
    • Central-upwind schemes for the Saint-Venant system
    • Kurganov A., and Levy D. Central-upwind schemes for the Saint-Venant system. Math. Model. Numer. Anal. 36 (2002) 397-425
    • (2002) Math. Model. Numer. Anal. , vol.36 , pp. 397-425
    • Kurganov, A.1    Levy, D.2
  • 23
    • 0001315315 scopus 로고    scopus 로고
    • Balancing source terms and flux gradients in high-resolution Godunov methods: the quasi-steady wave-propagation algorithm
    • Leveque R.J. Balancing source terms and flux gradients in high-resolution Godunov methods: the quasi-steady wave-propagation algorithm. J. Comput. Phys. 146 (1998) 346-365
    • (1998) J. Comput. Phys. , vol.146 , pp. 346-365
    • Leveque, R.J.1
  • 24
    • 0031128396 scopus 로고    scopus 로고
    • Tidal flow and transport modeling using ultimate quickest scheme
    • Lin B., and Falconer R.A. Tidal flow and transport modeling using ultimate quickest scheme. J. Hydraulic Eng. 123 (1997) 303-314
    • (1997) J. Hydraulic Eng. , vol.123 , pp. 303-314
    • Lin, B.1    Falconer, R.A.2
  • 27
    • 0042236790 scopus 로고    scopus 로고
    • The improved surface gradient method for flows simulation in variable bed topography channel using TVD-MacCormack scheme
    • Ming-Hen T. The improved surface gradient method for flows simulation in variable bed topography channel using TVD-MacCormack scheme. Int. J. Numer. Methods Fluids 43 (2003) 71-91
    • (2003) Int. J. Numer. Methods Fluids , vol.43 , pp. 71-91
    • Ming-Hen, T.1
  • 28
    • 85190091157 scopus 로고    scopus 로고
    • K. Mohamed, Simulation numérique des systèmes non homogènes, PhD. Thesis, Université de Paris 13, 2005.
  • 29
    • 0033520121 scopus 로고    scopus 로고
    • Positivity preserving finite volume Roe schemes for transport-diffusion equations
    • Monthe L.A., Benkhaldoun F., and Elmahi I. Positivity preserving finite volume Roe schemes for transport-diffusion equations. Comput. Methods Appl. Mech. Eng. 178 (1999) 215-232
    • (1999) Comput. Methods Appl. Mech. Eng. , vol.178 , pp. 215-232
    • Monthe, L.A.1    Benkhaldoun, F.2    Elmahi, I.3
  • 30
    • 5144234460 scopus 로고    scopus 로고
    • A particle-tracking model for simulating pollutant dispersion in the Strait of Gibraltar
    • Periáñez R. A particle-tracking model for simulating pollutant dispersion in the Strait of Gibraltar. Marine Pollut. Bull. 49 (2004) 613-623
    • (2004) Marine Pollut. Bull. , vol.49 , pp. 613-623
    • Periáñez, R.1
  • 31
    • 0012588539 scopus 로고    scopus 로고
    • A kinetic scheme for the Saint-Venant system with a source term
    • Perthame B., and Simeoni C. A kinetic scheme for the Saint-Venant system with a source term. CALCOLO 38 (2001) 201-231
    • (2001) CALCOLO , vol.38 , pp. 201-231
    • Perthame, B.1    Simeoni, C.2
  • 32
    • 2942757053 scopus 로고
    • Approximate Riemann solvers, parameter vectors and difference schemes
    • Roe P.L. Approximate Riemann solvers, parameter vectors and difference schemes. J. Comp. Phys. 43 (1981) 357-372
    • (1981) J. Comp. Phys. , vol.43 , pp. 357-372
    • Roe, P.L.1
  • 33
    • 85190113763 scopus 로고    scopus 로고
    • S. Sahmim, F. Benkhaldoun, F. Alcrudo, A sign matrix based scheme for quasi-hyperbolic non-homogeneous PDEs with an analysis of the convergence stagnation problem, J. Comp. Phys. (2007), submitted for publication.
  • 34
    • 85190135978 scopus 로고    scopus 로고
    • S. Sahmim, F. Benkhaldoun, Schéma SRNHS: Analyse et Application d'un Schéma aux Volume Finis dédié aux Systémes non Homogénes, ARIMA. 5, 302-316 (2006). .
  • 35
    • 5044227412 scopus 로고    scopus 로고
    • Non-oscillatory relaxation methods for the shallow water equations in one and two space dimensions
    • Seai{dotless}̈d M. Non-oscillatory relaxation methods for the shallow water equations in one and two space dimensions. Int. J. Numer. Methods Fluids 46 (2004) 457-484
    • (2004) Int. J. Numer. Methods Fluids , vol.46 , pp. 457-484
    • Seaïd, M.1
  • 37
    • 0348194970 scopus 로고    scopus 로고
    • Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry
    • Vázquez M.E. Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry. J. Comp. Phys. 148 (1999) 497-526
    • (1999) J. Comp. Phys. , vol.148 , pp. 497-526
    • Vázquez, M.E.1
  • 38
    • 0001906210 scopus 로고
    • A comparative study of computational methods in cosmic gas dynamics
    • Van Albada G.D., Van Leer B., and Roberts W.W. A comparative study of computational methods in cosmic gas dynamics. Astron. Astrophys. 108 (1982) 76-93
    • (1982) Astron. Astrophys. , vol.108 , pp. 76-93
    • Van Albada, G.D.1    Van Leer, B.2    Roberts, W.W.3
  • 39
    • 0036647452 scopus 로고    scopus 로고
    • ENO and WENO schemes with the exact conservation property for one-dimensional shallow-water equations
    • Vukovic S., and Sopta L. ENO and WENO schemes with the exact conservation property for one-dimensional shallow-water equations. J. Comp. Phys. 179 (2002) 593-621
    • (2002) J. Comp. Phys. , vol.179 , pp. 593-621
    • Vukovic, S.1    Sopta, L.2
  • 40
    • 33644933296 scopus 로고    scopus 로고
    • High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms
    • Xing Y., and Shu C. High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms. J. Comp. Phys. 214 (2006) 567-598
    • (2006) J. Comp. Phys. , vol.214 , pp. 567-598
    • Xing, Y.1    Shu, C.2
  • 41
    • 0002690008 scopus 로고    scopus 로고
    • The surface gradient method for the treatment of source terms in the shallow water equations
    • Zhou J.G., Causon D.M., Mingham C.G., and Ingram D.M. The surface gradient method for the treatment of source terms in the shallow water equations. J. Comp. Phys. 20 (2001) 1-25
    • (2001) J. Comp. Phys. , vol.20 , pp. 1-25
    • Zhou, J.G.1    Causon, D.M.2    Mingham, C.G.3    Ingram, D.M.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.