메뉴 건너뛰기




Volumn 231, Issue 20, 2012, Pages 6861-6906

Augmented versions of the HLL and HLLC Riemann solvers including source terms in one and two dimensions for shallow flow applications

Author keywords

Augmented solver; HLL; HLLC; Roe; Shallow water; Source terms; Stability region; Weak solutions; Well balanced approach; Wet dry front

Indexed keywords

FLOODS;

EID: 84864564584     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2012.06.031     Document Type: Article
Times cited : (76)

References (35)
  • 1
    • 0000935266 scopus 로고
    • A finite difference method for the computation of discontinuous solutions of the equations of fluid dynamics
    • Godunov S.K. A finite difference method for the computation of discontinuous solutions of the equations of fluid dynamics. Mater. Sb. 1959, 47:357-393.
    • (1959) Mater. Sb. , vol.47 , pp. 357-393
    • Godunov, S.K.1
  • 2
    • 0000876320 scopus 로고
    • On upstream differencing and Godunov type methods for hyperbolic conservation laws
    • Harten A., Lax P., van Leer B. On upstream differencing and Godunov type methods for hyperbolic conservation laws. SIAM Rev. 1983, 25:35-61.
    • (1983) SIAM Rev. , vol.25 , pp. 35-61
    • Harten, A.1    Lax, P.2    van Leer, B.3
  • 3
    • 2942757053 scopus 로고
    • Approximate Riemann solvers, parameter vectors, and difference schemes
    • Roe P.L. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 1981, 43:357-372.
    • (1981) J. Comput. Phys. , vol.43 , pp. 357-372
    • Roe, P.L.1
  • 4
    • 0003122153 scopus 로고
    • Restoration of the contact surface in the HLL Riemann solver
    • Toro E.F., Spruce M., Spears W. Restoration of the contact surface in the HLL Riemann solver. Shock Waves 1994, 4:25-34.
    • (1994) Shock Waves , vol.4 , pp. 25-34
    • Toro, E.F.1    Spruce, M.2    Spears, W.3
  • 5
    • 0028534347 scopus 로고
    • Upwind methods for hyperbolic conservation laws with source terms
    • Bermudez A., Vázquez-Cendón M.E. Upwind methods for hyperbolic conservation laws with source terms. Comput. Fluids. 1994, 23:1049-1071.
    • (1994) Comput. Fluids. , vol.23 , pp. 1049-1071
    • Bermudez, A.1    Vázquez-Cendón, M.E.2
  • 6
    • 0033838423 scopus 로고    scopus 로고
    • On the numerical treatment of the source terms in the shallow water equations
    • García-Navarro P., Vázquez-Cendón M.E. On the numerical treatment of the source terms in the shallow water equations. Comput. Fluids. 2000, 29:951-979.
    • (2000) Comput. Fluids. , vol.29 , pp. 951-979
    • García-Navarro, P.1    Vázquez-Cendón, M.E.2
  • 7
    • 0011032642 scopus 로고    scopus 로고
    • Flux difference splitting and the balancing of source terms and flux gradients
    • Hubbard M.E., García-Navarro P. Flux difference splitting and the balancing of source terms and flux gradients. J. Comput. Phys. 2000, 165:89-125.
    • (2000) J. Comput. Phys. , vol.165 , pp. 89-125
    • Hubbard, M.E.1    García-Navarro, P.2
  • 8
    • 77953572225 scopus 로고    scopus 로고
    • Simple and efficient solution of the shallow water equations with source terms
    • Lee S.H., Wright N.G. Simple and efficient solution of the shallow water equations with source terms. Int. J. Numer. Meth. Fluids. 2010, 63:313-340.
    • (2010) Int. J. Numer. Meth. Fluids. , vol.63 , pp. 313-340
    • Lee, S.H.1    Wright, N.G.2
  • 9
    • 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., Ingram D.M. The surface gradient method for the treatment of source terms in the shallow-water equations. J. Comput. Phys. 2001, 168:1-25.
    • (2001) J. Comput. Phys. , vol.168 , pp. 1-25
    • Zhou, J.G.1    Causon, D.M.2    Mingham, C.G.3    Ingram, D.M.4
  • 10
    • 55949108414 scopus 로고    scopus 로고
    • Adaptive quadtree simulation of shallow flows with wet-dry fronts over complex topography
    • Liang Q., Borthwick A.G.L. Adaptive quadtree simulation of shallow flows with wet-dry fronts over complex topography. Comput. Fluids. 2009, 38:221-234.
    • (2009) Comput. Fluids. , vol.38 , pp. 221-234
    • Liang, Q.1    Borthwick, A.G.L.2
  • 11
    • 19044370217 scopus 로고    scopus 로고
    • High order finite difference WENO schemes with the exact conservation property for the shallow water equations
    • Yulong X., Chi-Wang S. High order finite difference WENO schemes with the exact conservation property for the shallow water equations. J. Comput. Phys. 2005, 208:206-227.
    • (2005) J. Comput. Phys. , vol.208 , pp. 206-227
    • Yulong, X.1    Chi-Wang, S.2
  • 12
    • 0035399783 scopus 로고    scopus 로고
    • Exact solutions to the Riemann problem of the shallow water equations with a bottom step
    • Alcrudo F., Benkhaldoun F. Exact solutions to the Riemann problem of the shallow water equations with a bottom step. Comput. Fluids. 2001, 30:643-671.
    • (2001) Comput. Fluids. , vol.30 , pp. 643-671
    • Alcrudo, F.1    Benkhaldoun, F.2
  • 13
    • 38749099435 scopus 로고    scopus 로고
    • Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometry
    • Bernetti R., Titarev V.A., Toro E.F. Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometry. J. Comput. Phys. 2008, 227:3212-3243.
    • (2008) J. Comput. Phys. , vol.227 , pp. 3212-3243
    • Bernetti, R.1    Titarev, V.A.2    Toro, E.F.3
  • 15
    • 67349101335 scopus 로고    scopus 로고
    • Numerical resolution of well-balanced shallow water equations with complex source terms
    • Liang Q., Marche F. Numerical resolution of well-balanced shallow water equations with complex source terms. Adv. Water Res. 2009, 32:873-884.
    • (2009) Adv. Water Res. , vol.32 , pp. 873-884
    • Liang, Q.1    Marche, F.2
  • 16
    • 67349116002 scopus 로고    scopus 로고
    • Conservative numerical simulation of multicomponent transport in two-dimensional unsteady shallow water flow
    • Murillo J., García-Navarro P., Burguete J. Conservative numerical simulation of multicomponent transport in two-dimensional unsteady shallow water flow. J. Comput. Phys. 2009, 228:5539-5573.
    • (2009) J. Comput. Phys. , vol.228 , pp. 5539-5573
    • Murillo, J.1    García-Navarro, P.2    Burguete, J.3
  • 17
    • 84980076280 scopus 로고
    • On the solution of nonlinear hyperbolic differential equations by finite differences
    • Courant R., Isaacson E., Rees M. On the solution of nonlinear hyperbolic differential equations by finite differences. Commun. Pure Appl. Maths. 1952, 5:243-255.
    • (1952) Commun. Pure Appl. Maths. , vol.5 , pp. 243-255
    • Courant, R.1    Isaacson, E.2    Rees, M.3
  • 18
    • 39549095826 scopus 로고    scopus 로고
    • Time step restrictions for well balanced shallow water solutions in non-zero velocity steady states
    • Murillo J., García-Navarro P., Burguete J. Time step restrictions for well balanced shallow water solutions in non-zero velocity steady states. Int. J. Numer. Meth. Fluids. 2008, 56:661-686.
    • (2008) Int. J. Numer. Meth. Fluids. , vol.56 , pp. 661-686
    • Murillo, J.1    García-Navarro, P.2    Burguete, J.3
  • 19
    • 48749145227 scopus 로고
    • Self adjusting grid methods for one-dimensional hyperbolic conservation laws
    • Harten A., Hyman J.M. Self adjusting grid methods for one-dimensional hyperbolic conservation laws. J. Comput. Phys. 1983, 50:235-269.
    • (1983) J. Comput. Phys. , vol.50 , pp. 235-269
    • Harten, A.1    Hyman, J.M.2
  • 20
    • 38949110674 scopus 로고    scopus 로고
    • Augmented Riemann solvers for the shallow water equations over variable topography with steady states and inundation
    • George D.L. Augmented Riemann solvers for the shallow water equations over variable topography with steady states and inundation. J. Comput. Phys. 2008, 227:3089-3113.
    • (2008) J. Comput. Phys. , vol.227 , pp. 3089-3113
    • George, D.L.1
  • 21
    • 67349095105 scopus 로고    scopus 로고
    • Generalized Roe schemes for 1D two-phase, free-surface flows over a mobile bed
    • Rosatti G., Murillo J., Fraccarollo L. Generalized Roe schemes for 1D two-phase, free-surface flows over a mobile bed. J. Comput. Phys. 2007, 54:543-590.
    • (2007) J. Comput. Phys. , vol.54 , pp. 543-590
    • Rosatti, G.1    Murillo, J.2    Fraccarollo, L.3
  • 22
    • 77950041338 scopus 로고    scopus 로고
    • Weak solutions for partial differential equations with source terms: application to the shallow water equations
    • Murillo J., García-Navarro P. Weak solutions for partial differential equations with source terms: application to the shallow water equations. J. Comput. Phys. 2010, 229:4327-4368.
    • (2010) J. Comput. Phys. , vol.229 , pp. 4327-4368
    • Murillo, J.1    García-Navarro, P.2
  • 23
    • 57849121562 scopus 로고    scopus 로고
    • Friction term discretization and limitation to preserve stability and conservation in the 1D shallow-water model: application to unsteady irrigation and river flow
    • Burguete J., García-Navarro P., Murillo J. Friction term discretization and limitation to preserve stability and conservation in the 1D shallow-water model: application to unsteady irrigation and river flow. Int. J. Numer. Meth. Fluids. 2008, 58:403-425.
    • (2008) Int. J. Numer. Meth. Fluids. , vol.58 , pp. 403-425
    • Burguete, J.1    García-Navarro, P.2    Murillo, J.3
  • 24
    • 84855192541 scopus 로고    scopus 로고
    • Wave Riemann description of friction terms in unsteady shallow flows: application to water and mud/debris floods
    • Murillo J., García-Navarro P. Wave Riemann description of friction terms in unsteady shallow flows: application to water and mud/debris floods. J. Comput. Phys. 2011, 231:1963-2001.
    • (2011) J. Comput. Phys. , vol.231 , pp. 1963-2001
    • Murillo, J.1    García-Navarro, P.2
  • 25
    • 0001674149 scopus 로고
    • Simplified second-order Godunov-type methods
    • Davis S.F. Simplified second-order Godunov-type methods. SIAM J. Sci. Stat. Comput. 1988, 9:445-473.
    • (1988) SIAM J. Sci. Stat. Comput. , vol.9 , pp. 445-473
    • Davis, S.F.1
  • 26
    • 0001394094 scopus 로고
    • On Godunov-type methods for gas dynamics
    • Einfeldt B. On Godunov-type methods for gas dynamics. SIAM J. Numer. Anal. 1988, 25:294-318.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 294-318
    • Einfeldt, B.1
  • 31
    • 0348194970 scopus 로고    scopus 로고
    • Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry
    • Vázquez-Cendón M.E. Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry. J. Comput. Phys. 1999, 148:497-498.
    • (1999) J. Comput. Phys. , vol.148 , pp. 497-498
    • Vázquez-Cendón, M.E.1
  • 33
    • 0027100001 scopus 로고
    • Numerical solution of the shallow water equations on a beach using the weighted average flux method
    • Watson G., Peregrine D.H., Toro E.F. Numerical solution of the shallow water equations on a beach using the weighted average flux method. Comput. Fluid Dyn. 1992, 1:495-502.
    • (1992) Comput. Fluid Dyn. , vol.1 , pp. 495-502
    • Watson, G.1    Peregrine, D.H.2    Toro, E.F.3
  • 35
    • 0019382973 scopus 로고
    • Some exact solutions to the nonlinear shallow water equations
    • Thacker W.C. Some exact solutions to the nonlinear shallow water equations. J. Fluid Mech. 1981, 107:499-508.
    • (1981) J. Fluid Mech. , vol.107 , pp. 499-508
    • Thacker, W.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.