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Volumn 42, Issue 5, 2008, Pages 851-885

A Roe-type scheme for two-phase shallow granular flows over variable topography

Author keywords

Finite volume schemes; Granular flows; Non conservative systems; Numerical model; Riemann solvers; Thin layer approximation; Two phase flows; Well balanced schemes

Indexed keywords


EID: 49949103892     PISSN: 0764583X     EISSN: 12903841     Source Type: Journal    
DOI: 10.1051/m2an:2008029     Document Type: Article
Times cited : (125)

References (56)
  • 1
    • 33947335754 scopus 로고
    • A fluid-dynamical description of fluidized beds: Equations of motion
    • T.B. Anderson and R. Jackson, A fluid-dynamical description of fluidized beds: Equations of motion. Ind. Eng. Chem. Fundam. 6 (1967) 527-539.
    • (1967) Ind. Eng. Chem. Fundam , vol.6 , pp. 527-539
    • Anderson, T.B.1    Jackson, R.2
  • 2
    • 4644342716 scopus 로고    scopus 로고
    • A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows
    • E. Audusse, F. Bouchut, M.-O. Bristeau, R. Klein and B. Perthame, A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comput. 25 (2004) 2050-2065.
    • (2004) SIAM J. Sci. Comput , vol.25 , pp. 2050-2065
    • Audusse, E.1    Bouchut, F.2    Bristeau, M.-O.3    Klein, R.4    Perthame, B.5
  • 3
    • 0038746749 scopus 로고    scopus 로고
    • A wave-propagation method for conservation laws and balance laws with spatially varying flux functions
    • D. Bale, R.J. LeVeque, S. Mitran and J.A. Rossmanith, A wave-propagation method for conservation laws and balance laws with spatially varying flux functions. SIAM J. Sci. Comput. 24 (2002) 955-978.
    • (2002) SIAM J. Sci. Comput , vol.24 , pp. 955-978
    • Bale, D.1    LeVeque, R.J.2    Mitran, S.3    Rossmanith, J.A.4
  • 5
    • 29244451795 scopus 로고    scopus 로고
    • Gravity driven shallow water models for arbitrary topography
    • F. Bouchut and M. Westdickenberg, Gravity driven shallow water models for arbitrary topography. Comm. Math. Sci. 2 (2004) 359-389.
    • (2004) Comm. Math. Sci , vol.2 , pp. 359-389
    • Bouchut, F.1    Westdickenberg, M.2
  • 6
    • 0035631410 scopus 로고    scopus 로고
    • A Q-scheme for a class of systems of coupled conservation, laws with source term. Application, to a two-layer 1-D shallow water system
    • M.J. Castro, J. Macías and C. Parés, A Q-scheme for a class of systems of coupled conservation, laws with source term. Application, to a two-layer 1-D shallow water system. ESAIM: M2AN 35 (2001) 107-127.
    • (2001) ESAIM: M2AN , vol.35 , pp. 107-127
    • Castro, M.J.1    Macías, J.2    Parés, C.3
  • 8
    • 0035093201 scopus 로고    scopus 로고
    • Flow of variably fluidized granular masses across three-dimensional terrain: 2. Numerical predictions and experimental tests
    • R.P. Denlinger and. R.M. Iverson, Flow of variably fluidized granular masses across three-dimensional terrain: 2. Numerical predictions and experimental tests. J. Geophys. Res. 106 (2001) 553-566.
    • (2001) J. Geophys. Res , vol.106 , pp. 553-566
    • Denlinger, R.P.1    Iverson, R.M.2
  • 9
    • 3342943656 scopus 로고    scopus 로고
    • Granular avalanches across irregular three-dimensional terrain: 1, Theory and computation
    • doi: 10.1029/2003JF000085
    • R.P. Denlinger and R.M. Iverson, Granular avalanches across irregular three-dimensional terrain: 1, Theory and computation. J. Geophys. Res. 109 (2004) F01014, doi: 10.1029/2003JF000085.
    • (2004) J. Geophys. Res , vol.109
    • Denlinger, R.P.1    Iverson, R.M.2
  • 10
    • 0037404907 scopus 로고    scopus 로고
    • Some approximate Godunov schemes to compute shallow-water equations with topography
    • T. Gallouët, J.-M Hérard and N. Seguin, Some approximate Godunov schemes to compute shallow-water equations with topography. Comput. Fluids 32 (2003) 479-513.
    • (2003) Comput. Fluids , vol.32 , pp. 479-513
    • Gallouët, T.1    Hérard, J.-M.2    Seguin, N.3
  • 13
    • 0034209981 scopus 로고    scopus 로고
    • L. Gosse, A. well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms. Comput. Math. Appl. 39 (2000) 135-159.
    • L. Gosse, A. well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms. Comput. Math. Appl. 39 (2000) 135-159.
  • 15
    • 33746445883 scopus 로고    scopus 로고
    • Gravity driven free surface flow of granular avalanches over complex basal topography
    • J.M.N.T. Gray, M. Wieland and K. Hutter, Gravity driven free surface flow of granular avalanches over complex basal topography. Proc. R. Soc. London S. A 455 (1999) 1841-1874.
    • (1999) Proc. R. Soc. London S. A , vol.455 , pp. 1841-1874
    • Gray, J.M.N.T.1    Wieland, M.2    Hutter, K.3
  • 16
    • 1542576141 scopus 로고    scopus 로고
    • A well-balanced scheme for the numerical processing of source terms in hyperbolic equations
    • J.M. Greenberg and A. Y. LeRoux, A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J. Numer. Anal. 33 (1996) 1-16.
    • (1996) SIAM J. Numer. Anal , vol.33 , pp. 1-16
    • Greenberg, J.M.1    LeRoux, A.Y.2
  • 17
    • 48749145227 scopus 로고
    • Self-adjusting grid methods for one-dimensional hyperbolic conservation, laws
    • A. Harten, and J.M. Hyman, Self-adjusting grid methods for one-dimensional hyperbolic conservation, laws. J. Comput. Phys. 50 (1983) 235-269.
    • (1983) J. Comput. Phys , vol.50 , pp. 235-269
    • Harten, A.1    Hyman, J.M.2
  • 18
    • 0027790109 scopus 로고
    • Two-dimensional spreading of a granular avalanche down an inclined plane, part I. Theory
    • K. Hutter, M. Siegel, S.B. Savage and Y. Nohguchi, Two-dimensional spreading of a granular avalanche down an inclined plane, part I. Theory. Acta Mech. 100 (1993) 37-68.
    • (1993) Acta Mech , vol.100 , pp. 37-68
    • Hutter, K.1    Siegel, M.2    Savage, S.B.3    Nohguchi, Y.4
  • 19
    • 0031414779 scopus 로고    scopus 로고
    • The physics of debris flows
    • R.M. Iverson, The physics of debris flows. Rev. Geophys. 35 (1997) 245-296.
    • (1997) Rev. Geophys , vol.35 , pp. 245-296
    • Iverson, R.M.1
  • 20
    • 0035092403 scopus 로고    scopus 로고
    • Flow of variably fluidized granular masses across three-dimensional terrain: 1, Coulomb mixture theory
    • R.M. Iverson and R.P. Denlinger, Flow of variably fluidized granular masses across three-dimensional terrain: 1, Coulomb mixture theory. J. Geophys. Res. 106 (2001) 537-552.
    • (2001) J. Geophys. Res , vol.106 , pp. 537-552
    • Iverson, R.M.1    Denlinger, R.P.2
  • 21
    • 3342943656 scopus 로고    scopus 로고
    • Granular avalanches across irregular three-dimensional terrain: 2, Experimental tests
    • doi:10.1029/2003JF000084
    • R.M. Iverson, M. Logan and R.P. Denlinger, Granular avalanches across irregular three-dimensional terrain: 2, Experimental tests. J. Geophys. Res. 109 (2004) F01015, doi:10.1029/2003JF000084.
    • (2004) J. Geophys. Res , vol.109
    • Iverson, R.M.1    Logan, M.2    Denlinger, R.P.3
  • 22
    • 0036501254 scopus 로고    scopus 로고
    • The mobility of long-runout landslides
    • F. Legros, The mobility of long-runout landslides. Eng. Geol. 63 (2002) 301-331.
    • (2002) Eng. Geol , vol.63 , pp. 301-331
    • Legros, F.1
  • 23
    • 49949098673 scopus 로고    scopus 로고
    • R.J. LeVeque, CLAWPACK. http://www.amath.washington.edu/~claw.
    • R.J. LeVeque, CLAWPACK. http://www.amath.washington.edu/~claw.
  • 24
    • 0000308880 scopus 로고    scopus 로고
    • Wave propagation algorithms for multi-dimensional hyperbolic systems
    • R.J. LeVeque, Wave propagation algorithms for multi-dimensional hyperbolic systems. J. Comput. Phys. 131 (1997) 327-353.
    • (1997) J. Comput. Phys , vol.131 , pp. 327-353
    • LeVeque, R.J.1
  • 25
    • 0001315315 scopus 로고    scopus 로고
    • Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wavepropagation algorithm
    • R.J. LeVeque, Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wavepropagation algorithm. J. Comput. Phys. 146 (1998) 346-365.
    • (1998) J. Comput. Phys , vol.146 , pp. 346-365
    • LeVeque, R.J.1
  • 27
    • 49949116516 scopus 로고    scopus 로고
    • R.J. LeVeque and. D.L. George, High-resolution finite methods for the shallow water equations with, bathymetry and dry states, in Proceedings of Long-Wave Workshop, Catalina, 2004, P.L.-F. Liu, H. Yen and C. Synolakis Eds., Advances Numerical Models for Simulating Tsunami Waves and Runup, Advances in Coastal and Ocean Engineering 10, World Scientific (2008) 43-73.
    • R.J. LeVeque and. D.L. George, High-resolution finite volume methods for the shallow water equations with, bathymetry and dry states, in Proceedings of Long-Wave Workshop, Catalina, 2004, P.L.-F. Liu, H. Yen and C. Synolakis Eds., Advances Numerical Models for Simulating Tsunami Waves and Runup, Advances in Coastal and Ocean Engineering 10, World Scientific (2008) 43-73.
  • 28
    • 0035922233 scopus 로고    scopus 로고
    • A class of approximate Riemann solvers and their relation to relaxation schemes
    • R.J. LeVeque and M. Pelanti, A class of approximate Riemann solvers and their relation to relaxation schemes. J. Comput. Phys. 172 (2001) 572-591.
    • (2001) J. Comput. Phys , vol.172 , pp. 572-591
    • LeVeque, R.J.1    Pelanti, M.2
  • 29
    • 34548349100 scopus 로고    scopus 로고
    • Numerical modeling of self-channeling granular flows and of their levee-channel deposits
    • doi: 10.1029/2006JF000469
    • A. Mangeney, F. Bouchut, N. Thomas, J.-P. Vilotte and M.-O. Bristeau, Numerical modeling of self-channeling granular flows and of their levee-channel deposits. J. Geophys. Res. 112 (2007) F02017, doi: 10.1029/2006JF000469.
    • (2007) J. Geophys. Res , vol.112
    • Mangeney, A.1    Bouchut, F.2    Thomas, N.3    Vilotte, J.-P.4    Bristeau, M.-O.5
  • 32
    • 0037374881 scopus 로고    scopus 로고
    • Constitutive relations for the interaction force in multicomponent particulate flows
    • M. Massoudi, Constitutive relations for the interaction force in multicomponent particulate flows. Int.. J. Non-Linear Mech. 38 (2003) 313-336.
    • (2003) Int.. J. Non-Linear Mech , vol.38 , pp. 313-336
    • Massoudi, M.1
  • 33
    • 32644433341 scopus 로고    scopus 로고
    • Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows
    • S. Noelle, N. Pankratz, G. Puppo and J.R. Natvig, Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows. J. Comput. Phys. 213 (2006) 474-499.
    • (2006) J. Comput. Phys , vol.213 , pp. 474-499
    • Noelle, S.1    Pankratz, N.2    Puppo, G.3    Natvig, J.R.4
  • 34
    • 10044294949 scopus 로고    scopus 로고
    • On the well-balance property of Roe's method for nonconservative hyperbolic systems. Applications to shallow-water systems
    • C. Parés and M.J. Castro, On the well-balance property of Roe's method for nonconservative hyperbolic systems. Applications to shallow-water systems. ESAIM: MaAN 38 (2004) 821-852.
    • (2004) ESAIM: MaAN , vol.38 , pp. 821-852
    • Parés, C.1    Castro, M.J.2
  • 37
    • 34447276613 scopus 로고    scopus 로고
    • High-resolution finite volume methods for dusty gas jets and plumes
    • M. Pelanti and R.J. LeVeque, High-resolution finite volume methods for dusty gas jets and plumes. SIAM J. Sci. Comput. 28 (2006) 1335 1360.
    • (2006) SIAM J. Sci. Comput , vol.28 , pp. 1335-1360
    • Pelanti, M.1    LeVeque, R.J.2
  • 38
    • 23844543355 scopus 로고    scopus 로고
    • A two-fluid model for avalanche and debris flows
    • E.B. Pitman and L. Le, A two-fluid model for avalanche and debris flows. Phil. Tnms. R. Soc. A 363 (2005) 1573-1601.
    • (2005) Phil. Tnms. R. Soc. A , vol.363 , pp. 1573-1601
    • Pitman, E.B.1    Le, L.2
  • 40
    • 0347031385 scopus 로고    scopus 로고
    • Rapid shear flows of dry granular masses down curved and twisted channels
    • S.P. Pudasaini and K. Hutter, Rapid shear flows of dry granular masses down curved and twisted channels. J. Fluid Mech. 495 (2003) 193-208.
    • (2003) J. Fluid Mech , vol.495 , pp. 193-208
    • Pudasaini, S.P.1    Hutter, K.2
  • 42
    • 23844486721 scopus 로고    scopus 로고
    • Rapid motions of free-surface avalanches down curved and twisted channels and their numerical simulations
    • S.P. Pudasaini, Y. Wang and K. Hutter, Rapid motions of free-surface avalanches down curved and twisted channels and their numerical simulations. Phil. Trans. R. Soc. A 363 (2005) 1551-1571.
    • (2005) Phil. Trans. R. Soc. A , vol.363 , pp. 1551-1571
    • Pudasaini, S.P.1    Wang, Y.2    Hutter, K.3
  • 43
    • 0001827608 scopus 로고
    • On the stability of loose earth
    • W.J.M. Rankine, On the stability of loose earth. Phil. Trans. R. Soc. 147 (1857) 9-27.
    • (1857) Phil. Trans. R. Soc , vol.147 , pp. 9-27
    • Rankine, W.J.M.1
  • 44
    • 2942757053 scopus 로고
    • Approximate Riemann solvers, parameter vectors, and difference schemes
    • P.L. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43 (1981) 357 372.
    • (1981) J. Comput. Phys , vol.43 , pp. 357-372
    • Roe, P.L.1
  • 45
    • 0024611991 scopus 로고
    • The motion of a finite mass of granular material down a rough incline
    • S.B. Savage and K. Hutter, The motion of a finite mass of granular material down a rough incline. J. Fluid. Mech. 199 (1989) 177-215.
    • (1989) J. Fluid. Mech , vol.199 , pp. 177-215
    • Savage, S.B.1    Hutter, K.2
  • 46
    • 0025721526 scopus 로고
    • The dynamics of avalanches of granular materials from initiation to runout, part I. Analysis
    • S.B. Savage and K. Hutter, The dynamics of avalanches of granular materials from initiation to runout, part I. Analysis. Acta Mech. 86 (1991) 201-223
    • (1991) Acta Mech , vol.86 , pp. 201-223
    • Savage, S.B.1    Hutter, K.2
  • 47
    • 0025093650 scopus 로고
    • On modelling phase transitions by means of rate-type constitutive equations, shock wave structure
    • I. Suliciu, On modelling phase transitions by means of rate-type constitutive equations, shock wave structure. Internat. J. Engrg. Sci. 28 (1990) 829-841.
    • (1990) Internat. J. Engrg. Sci , vol.28 , pp. 829-841
    • Suliciu, I.1
  • 48
    • 0026850598 scopus 로고
    • Some stability-instability problems in phase transitions modelled by piecewise linear elastic or viscoelastic constitutive equations
    • I. Suliciu, Some stability-instability problems in phase transitions modelled by piecewise linear elastic or viscoelastic constitutive equations. Internat. J. Engrg. Sci. 30 (1992) 483 494.
    • (1992) Internat. J. Engrg. Sci , vol.30 , pp. 483-494
    • Suliciu, I.1
  • 49
    • 0036151390 scopus 로고    scopus 로고
    • Shock-capturing and front-tacking methods for dry granular avalanches
    • Y.C. Tai, S. Noelle, J.M.N.T. Gray and K. Hutter, Shock-capturing and front-tacking methods for dry granular avalanches. J. Comput. Phys. 175 (2002) 269 301.
    • (2002) J. Comput. Phys , vol.175 , pp. 269-301
    • Tai, Y.C.1    Noelle, S.2    Gray, J.M.N.T.3    Hutter, K.4
  • 51
    • 0242497800 scopus 로고    scopus 로고
    • Methods for multiphase computational fluid dynamics
    • B.G.M. van Wachem and A.E. Almstedt, Methods for multiphase computational fluid dynamics. Chem. Eng. J. 96 (2003) 81-98.
    • (2003) Chem. Eng. J , vol.96 , pp. 81-98
    • van Wachem, B.G.M.1    Almstedt, A.E.2
  • 52
    • 0348194970 scopus 로고    scopus 로고
    • Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry
    • M.E. Vázquez-Cendón, Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry. J. Comput. Phys. 148 (1999) 497-526.
    • (1999) J. Comput. Phys , vol.148 , pp. 497-526
    • Vázquez-Cendón, M.E.1
  • 53
    • 3343000506 scopus 로고    scopus 로고
    • A shock-capturing wave-propagation method for dry and saturated granular flows
    • P. Vollmöller, A shock-capturing wave-propagation method for dry and saturated granular flows. J. Comput. Phys. 199 (2004) 150-174.
    • (2004) J. Comput. Phys , vol.199 , pp. 150-174
    • Vollmöller, P.1
  • 54
    • 0018314831 scopus 로고
    • Two-layer shallow-water flow in two dimensions, a numerical study
    • C.B. Vreugdenhil, Two-layer shallow-water flow in two dimensions, a numerical study. J. Comput. Phys. 33 (1979) 169 184.
    • (1979) J. Comput. Phys , vol.33 , pp. 169-184
    • Vreugdenhil, C.B.1
  • 55
    • 0033437830 scopus 로고    scopus 로고
    • A constitutive model of multiphase mixtures and its application in shearing flows of saturated solid-fluid mixtures
    • Y. Wang and K. Hutter, A constitutive model of multiphase mixtures and its application in shearing flows of saturated solid-fluid mixtures. Granul. Matter 1 (1999) 163-181.
    • (1999) Granul. Matter , vol.1 , pp. 163-181
    • Wang, Y.1    Hutter, K.2
  • 56
    • 0032704712 scopus 로고    scopus 로고
    • A constitutive theory of fluid-saturated granular materials and its application in gravitational flows
    • Y. Wang and K. Hutter, A constitutive theory of fluid-saturated granular materials and its application in gravitational flows. Rheol. Acta 38 (1999) 214-223.
    • (1999) Rheol. Acta , vol.38 , pp. 214-223
    • Wang, Y.1    Hutter, K.2


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