Numerical simulations of granular free-surface flows using smoothed particle hydrodynamics

Journal of Non-Newtonian Fluid Mechanics

Volumn 166, Issue 12-13, 2011, Pages 698-712

  Chambon, G ^a   Bouvarel, R ^a   Laigle, D ^a   Naaim, M ^a  

^a Cemagref   (France)

Author keywords

Chute flow; Free surface flow; Granular flow; Granular rheology; Gravity driven surge; SPH

Indexed keywords

CHUTE FLOW; FREE-SURFACE FLOW; GRANULAR FLOW; GRANULAR RHEOLOGY; GRAVITY-DRIVEN SURGE; SPH;

ELASTICITY; GRANULAR MATERIALS; HYDRODYNAMICS; NUMERICAL METHODS; RHEOLOGY; STRAIN RATE; SURFACES; TWO DIMENSIONAL; VISCOSITY;

PARTICLES (PARTICULATE MATTER);

EID: 79957440074     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2011.03.007     Document Type: Article

References (64)

1. Nedderman R.M., Tüzün U., Savage S.B., Houlsby G.T. The flow of granular materials - I Discharge rates from hoppers. Chem. Eng. Sci. 1982, 37:1597-1609.
2. Faug T., Naaim M., Naaim-Bouvet F. Experimental and numerical study of granular flow and fence interaction. Ann. Glaciol. 2004, 38:135-138.
3. Denlinger R.P., Iverson R.M. Granular avalanches across irregular three-dimensional terra: 1. Theory and computation. J. Geophys. Res. 2004, 109:F01014.
4. Hungr O. Simplified models of spreading flow of dry granular material. Can. Geotech. J. 2008, 45:1156-1168.
5. Staron L., Vilotte J.-P., Radjai F. Preavalanche instabilities in a granular pile. Phys. Rev. Lett. 2002, 89:204302.
6. Da Cruz F., Emam S., Prochnow M., Roux J.N., Chevoir F. Rheophysics of dense granular materials: Discrete simulation of plane shear flows. Phys. Rev. E 2005, 72:021309.
7. Rognon P.G., Roux J.-N., Naaim M., Chevoir F. Dense flows of bidisperse assemblies of disks down an inclined plane. Phys. Fluids 2007, 19:058101.
8. Radjai F., Roux S., Moreau J.J. Contact forces in a granular packing. Chaos 1999, 9:544-550.
9. Savage S.B., Hutter K. The motion of a finite mass of granular material down a rough incline. J. Fluid Mech. 1989, 199:177-215.
10. Mangeney A., Heinrich P., Roche R. Analytical solution for testing debris avalanche numerical model. Pure Appl. Geophys. 2000, 157:1081-1096.
11. Pouliquen O. On the shape of granular fronts down rough inclined planes. Phys. Fluids 1999, 11:1956-1958.
12. Pouliquen O., Forterre Y. Friction law for dense granular flows: application to the motion of a mass down a rough inclined plane. J. Fluid Mech. 2002, 453:133-151.
13. MiDi G.D.R. On dense granular flows. Eur. Phys. J. E 2004, 14:341-365.
14. Forterre Y., Pouliquen O. Flows of dense granular media. Annu. Rev. Fluid Mech. 2008, 40:1-24.
15. Hutter K., Wang Y., Pudasaini S.P. The Savage-Hutter avalanche model: how far can it be pushed?. Phil. Trans. R.S.A 2005, 363:1507-1528.
16. Jop P., Forterre Y., Pouliquen O. A constitutive law for dense granular flows. Nature 2006, 441:727-730.
17. Jop P., Forterre Y., Pouliquen O. Crucial role of sidewalls in granular surface flows: consequences for the rheology. J. Fluid Mech. 2005, 541:167-192.
18. Jop P. Hydrodynamic modeling of granular flows in a modified Couette cell. Phys. Rev. E 2008, 77:032301.
19. Gingold R.A., Monaghan J.J. Smoothed particle hydrodynamics: Theory and application to non-spherical stars. Mon. Notes R. Astronom. Soc. 1977, 181:375-389.
20. Monaghan J.J. Smoothed particle hydrodynamics. Annu. Rev. Astron. Astrophys. 1992, 30:543-574.
21. Morris J.P., Fox P.J., Zhu Y. Modeling low Reynolds number incompressible flows using SPH. J. Comput. Phys. 1997, 136:214-226.
22. Liu G.R., Liu M.B. Smoothed Particle Hydrodynamics - A Meshfree Particle Method 2003, World Scientific Publishing Company.
23. Monaghan J.J. An introduction to SPH. Comput. Phys. Commun. 1988, 48:89-96.
24. Cleary P.W., Prakash M. Discrete element modelling and smoothed particle hydrodynamics: Potential in the environmental sciences. Phil. Trans. R.S.A 2004, 362:2003-2030.
25. Gomez-Gesteira M., Rogers B.D., Dalrymple R.A., Crespo A.J.C. State-of-the-art of classical SPH for free-surface flows. J. Hydraul. Res. 2010, 48:6-27.
26. Sigalotti L.D.G., Klapp J., Sira E., Melean Y., Hasmy A. SPH simulation of time-dependent Poiseuille flow at low Reynolds numbers. J. Comput. Phys. 2003, 191:622-638.
27. Graham D.I., Hughes J.P. Accuracy of SPH viscous flow models. Int. J. Numer. Methods Fluids 2008, 56:1261-1269.
28. Basa M., Quinlan N.J., Lastiwka M. Robustness and accuracy of SPH formulations for viscous flow. Int. J. Numer. Methods Fluids 2009, 60:1127-1148.
29. Rodriguez-Paz M.X., Bonet J. A corrected smooth particle hydrodynamics method for the simulation of debris flows. Numer. Meth. Part. D.E. 2003, 20:140-163.
30. Laigle D., Lachamp P., Naaim M. SPH-based numerical investigation of mudflow and other complex fluid flow interactions with structures. Comput. Geosci. 2007, 11:297-306.
31. Zhu H.N., Martys N.S., Ferraris C., De Kee D. A numerical study of the flow of Bingham-like fluids in two-dimensional vane and cylinder rheometers using a smoothed particle hydrodynamics (SPH) based method. J. Non-Newton. Fluid 2010, 165:362-375.
32. Ellero M., Kröger M., Hess S. Viscoelastic flows studied by smoothed particle dynamics. J. Non-Newton. Fluid 2002, 105:35-51.
33. Ellero M., Tanner R.I. SPH simulations of transient viscoelastic flows at low Reynolds number. J. Non-Newton. Fluid 2005, 132:61-72.
34. Fang J.N., Owens R.G., Tacher L., Parriaux A. A numerical study of the SPH method for simulating transient viscoelastic free surface flows. J. Non-Newton. Fluid 2006, 139:68-84.
35. Gutfraind R., Savage S.B. Smoothed Particle Hydrodynamics for the simulation of broken-ice fields: Mohr-Coulomb-type rheology and frictional boundary conditions. J. Comput. Phys. 1997, 134:203-215.
36. Oger L., Savage S.B. Smoothed particle hydrodynamics for cohesive grains. Comp. Methods Appl. M. 1999, 180:169-183.
37. Colagrossi A., Landrini M. Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J. Comput. Phys. 2003, 191:448-475.
38. Ferrari A., Dumbser M., Toro E.F., Armanini A. A new 3D parallel SPH scheme for free surface flows. Comput. Fluids 2009, 38:1203-1217.
39. Cassar C., Nicolas M., Pouliquen O. Submarine granular flows down inclined planes. Phys. Fluids 2005, 17:103301.
40. Forterre Y., Pouliquen O. Long-surface-wave instability in dense granular flows. J. Fluid Mech. 2003, 486:21-50.
41. Forterre Y. Kapiza waves as a test for three-dimensional granular flow rheology. J. Fluid Mech. 2006, 563:123-132.
42. Goujon C., Dalloz-Dubrujeaud B., Thomas N. Bidisperse granular avalanches on inclined planes: A rich variety of behaviors. Eur. Phys. J. E 2007, 23:199-215.
43. Linares-Guerrero E., Goujon C., Zenit R. Increased mobility of bidisperse granular avalanches. J. Fluid Mech. 2007, 593:475-504.
44. Daerr A., Douady S. Two types of avalanche behaviour in granular media. Nature 1999, 399:241-243.
45. Jop P., Forterre Y., Pouliquen O. Initiation of granular surface flows in a narrow channel. Phys. Fluids 2007, 19:088102.
46. Pouliquen O., Forterre Y. A non-local rheology for dense granular flows. Phil. Trans. R. S. A 2009, 367:5091-5107.
47. Pouliquen O., Cassar C., Jop P., Forterre Y., Nicolas M. Flow of dense granular material: towards simple constitutive laws. J. Stat. Mech.-Theory E 2006, P07020.
48. Pailha M., Pouliquen O. A two-phase flow description of the initiation of underwater granular avalanches. J. Fluid Mech. 2009, 633:115-135.
49. A.J. Crespo, Application of the Smoothed Particle Hydrodynamics model SPHysics to free-surface hydrodynamics, Ph.D. thesis, Universidade de Vigo, 2008.
50. Monaghan J.J. Simulating free surface flows with SPH. J. Comput. Phys. 1994, 110:399-406.
51. Bonet J., Lok T.S.L. Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. Comp. Methods Appl. M. 1999, 180:97-115.
52. Monaghan J.J. Smoothed particle hydrodynamics. Rep. Progress Phys. 2005, 68:1703-1759.
53. Fang J.N., Parriaux A., Rentschler M., Ancey C. Improved SPH methods for simulating free surface flows of viscous fluids. Appl. Numer. Math. 2009, 59:251-271.
54. Vaughan G.L., Healy T.R., Bryan K.R., Sneyd A.D., Gorman R.M. Completeness, conservation and error in SPH for fluids. Int. J. Numer. Methods Fluids 2008, 56:37-62.
55. Cummins S.J., Rudman M. An SPH projection method. J. Comput. Phys. 1999, 152:584-607.
56. Shao S., Lo E.Y.M. Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free-surface. Adv. Water Res. 2003, 26:787-800.
57. Lee E.S., Moulinec C., Xu R., Violeau D., Laurence D., Stansby P. Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method. J. Comput. Phys. 2008, 227:8417-8436.
58. Hughes J.P., Graham D.I. Comparison of incompressible and weakly-compressible SPH models for free-surface water flows. J. Hydraul. Res. 2010, 48:105-117.
59. Monaghan J.J., Kos A. Solitary waves on a Cretan beach. J. Waterw. Port. C.-ASCE 1999, 125:145-154.
60. Monaghan J.J. SPH without a tensile instability. J. Comput. Phys. 2000, 159:290-311.
61. P. Lachamp, Modélisation numérique de l'effet d'un obstacle sur les écoulements de fluides à seuil par le méthode SPH, Ph.D. thesis, Université Joseph Fourier, Grenoble, 2003 (in French).
62. Pouliquen O. Scaling laws in granular flows down rough inclined planes. Phys. Fluids 1999, 11:542-548.
63. Hogg A.J., Pritchard D. The effects of hydraulic resistance on dam-break and other shallow inertial flows. J. Fluid Mech. 2004, 501:179-212.
64. Vola D., Babik F., Latch J.C. On a numerical strategy to compute gravity currents of non-Newtonian fluids. J. Comput. Phys. 2004, 201:397-420.