Free Access
Volume 42, Number 5, September-October 2008
Page(s) 851 - 885
DOI https://doi.org/10.1051/m2an:2008029
Published online 30 July 2008
  1. T.B. Anderson and R. Jackson, A fluid-dynamical description of fluidized beds: Equations of motion. Ind. Eng. Chem. Fundam. 6 (1967) 527–539. [Google Scholar]
  2. 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. [CrossRef] [MathSciNet] [Google Scholar]
  3. 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. [CrossRef] [MathSciNet] [Google Scholar]
  4. F. Bouchut, Nonlinear stability of finite volume methods for hyperbolic conservation laws, and well-balanced schemes for sources. Birkhäuser-Verlag (2004). [Google Scholar]
  5. F. Bouchut and M. Westdickenberg, Gravity driven shallow water models for arbitrary topography. Comm. Math. Sci. 2 (2004) 359–389. [Google Scholar]
  6. 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. [CrossRef] [EDP Sciences] [Google Scholar]
  7. M.J. Castro, J.A. García Rodríguez, J.M. González-Vida, J. Macías, C. Parés and M.E. Vázquez-Cendón, Numerical simulation of two layer shallow water flows through channels with irregular geometry. J. Comput. Phys. 195 (2004) 202–235. [Google Scholar]
  8. 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. [Google Scholar]
  9. 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. [CrossRef] [Google Scholar]
  10. 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. [CrossRef] [MathSciNet] [Google Scholar]
  11. D. Gidaspow, Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions. Academic Press, New York (1994). [Google Scholar]
  12. E. Godlewski and P.-A. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer-Verlag, New York (1996). [Google Scholar]
  13. 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. [Google Scholar]
  14. N. Goutal and F. Maurel, Proceedings of the 2nd Workshop on Dam-Break Wave Simulation. Technical report EDF-DER Report HE-43/97/016/B, Chatou, France (1997). [Google Scholar]
  15. 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. [CrossRef] [Google Scholar]
  16. 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. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  17. A. Harten and J.M. Hyman, Self-adjusting grid methods for one-dimensional hyperbolic conservation laws. J. Comput. Phys. 50 (1983) 235–269. [CrossRef] [MathSciNet] [Google Scholar]
  18. 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. [CrossRef] [MathSciNet] [Google Scholar]
  19. R.M. Iverson, The physics of debris flows. Rev. Geophys. 35 (1997) 245–296. [Google Scholar]
  20. 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. [CrossRef] [Google Scholar]
  21. 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. [CrossRef] [Google Scholar]
  22. F. Legros, The mobility of long-runout landslides. Eng. Geol. 63 (2002) 301–331. [Google Scholar]
  23. R.J. LeVeque, clawpack. http://www.amath.washington.edu/ claw+. [Google Scholar]
  24. R.J. LeVeque, Wave propagation algorithms for multi-dimensional hyperbolic systems. J. Comput. Phys. 131 (1997) 327–353. [Google Scholar]
  25. R.J. LeVeque, Balancing source terms and flux gradients in high-resolution Godunov methods: The quasi-steady wave-propagation algorithm. J. Comput. Phys. 146 (1998) 346–365. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  26. R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems. Cambridge University Press (2002). [Google Scholar]
  27. 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. Yeh 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. [Google Scholar]
  28. 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. [CrossRef] [MathSciNet] [Google Scholar]
  29. 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. [CrossRef] [Google Scholar]
  30. A. Mangeney-Castelnau, J.-P. Vilotte, M.-O. Bristeau, B. Perthame, F. Bouchut, C. Simeoni and S. Yernini, Numerical modeling of avalanches based on Saint-Venant equations using a kinetic scheme. J. Geophys. Res. 108 (2003) 2527, doi:10.1029/2002JB002024. [CrossRef] [Google Scholar]
  31. A. Mangeney-Castelnau, F. Bouchut, J.-P. Vilotte, E. Lajeunesse, A. Aubertin and M. Pirulli, On the use of Saint-Venant equations to simulate the spreading of a granular mass. J. Geophys. Res. 110 (2005) B09103, doi:10.1029/2004JB003161. [CrossRef] [Google Scholar]
  32. M. Massoudi, Constitutive relations for the interaction force in multicomponent particulate flows. Int. J. Non-Linear Mech. 38 (2003) 313–336. [CrossRef] [Google Scholar]
  33. 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. [CrossRef] [MathSciNet] [Google Scholar]
  34. 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: M2AN 38 (2004) 821–852. [CrossRef] [EDP Sciences] [Google Scholar]
  35. A.K. Patra, A.C. Bauer, C.C. Nichita, E.B. Pitman, M.F. Sheridan, M. Bursik, B. Rupp, A. Webber, A.J. Stinton, L.M. Namikawa and C.S. Renschler, Parallel adaptive numerical simulation of dry avalanches over natural terrain. J. Volcanology Geotherm. Res. 139 (2005) 1–21. [CrossRef] [Google Scholar]
  36. M. Pelanti, Wave Propagation Algorithms for Multicomponent Compressible Flows with Applications to Volcanic Jets. Ph.D. thesis, University of Washington, USA (2005). [Google Scholar]
  37. 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. [CrossRef] [MathSciNet] [Google Scholar]
  38. E.B. Pitman and L. Le, A two-fluid model for avalanche and debris flows. Phil. Trans. R. Soc. A 363 (2005) 1573–1601. [Google Scholar]
  39. E.B. Pitman, C.C. Nichita, A.K. Patra, A.C. Bauer, M.F. Sheridan and M. Bursik, Computing granular avalanches and landslides. Phys. Fluids 15 (2003) 3638–3646. [Google Scholar]
  40. 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. [CrossRef] [MathSciNet] [Google Scholar]
  41. S.P. Pudasaini, Y. Wang and K. Hutter, Modelling debris flows down general channels. Natural Hazards and Earth System Sciences 5 (2005) 799–819. [Google Scholar]
  42. 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. [CrossRef] [Google Scholar]
  43. W.J.M. Rankine, On the stability of loose earth. Phil. Trans. R. Soc. 147 (1857) 9–27. [Google Scholar]
  44. P.L. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43 (1981) 357–372. [Google Scholar]
  45. 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. [Google Scholar]
  46. 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. [CrossRef] [MathSciNet] [Google Scholar]
  47. I. Suliciu, On modelling phase transitions by means of rate-type constitutive equations, shock wave structure. Internat. J. Engrg. Sci. 28 (1990) 829–841. [Google Scholar]
  48. 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. [Google Scholar]
  49. 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. [CrossRef] [Google Scholar]
  50. E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer-Verlag, Berlin, Heidelberg (1997). [Google Scholar]
  51. B.G.M. van Wachem and A.E. Almstedt, Methods for multiphase computational fluid dynamics. Chem. Eng. J. 96 (2003) 81–98. [CrossRef] [Google Scholar]
  52. 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. [CrossRef] [MathSciNet] [Google Scholar]
  53. P. Vollmöller, A shock-capturing wave-propagation method for dry and saturated granular flows. J. Comput. Phys. 199 (2004) 150–174. [CrossRef] [Google Scholar]
  54. C.B. Vreugdenhil, Two-layer shallow-water flow in two dimensions, a numerical study. J. Comput. Phys. 33 (1979) 169–184. [CrossRef] [MathSciNet] [Google Scholar]
  55. 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. [Google Scholar]
  56. 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. [CrossRef] [Google Scholar]

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