Smoothed particle hydrodynamics (SPH) method adopts discrete particles for discretion of computational domain,and field variables and their spatial derivatives are evaluated by summation interpolation based on particle and kernel functions,which makes this method more suitable for processing the large displacement,movable boundary,and free surface problems.In order to analyze the dam break problem over movable bed,an erosion condition based on Drunker-Prager is used.The particles satisfying this condition will move with the non-Newtonian characteristic,i.e.,Herschel-Bulkley-Papanastasiou rheology,while the particles which do not satisfy the condition will remain still.In order to improve the results of numerical modelling further,a two-phase SPH method which is based on the ratio of volume is applied when modelling the dynamics of mixture,and the calculation of viscosity of mixture is improved based on the dynamic characters of solid-fluid mixture.A dam-break problem over movable bed is analyzed based on the model mentioned above.Numerical results are compared with the experimental data,and the comparison verifies that the proposed formula improves the results of numerical modelling.
QIAO Cheng
,
PAN Huali
,
OU Guoqiang
. Application of two-phase smoothed particle hydrodynamics method to dam break over movable bed[J]. Journal of University of Chinese Academy of Sciences, 2017
, 34(5)
: 625
-632
.
DOI: 10.7523/j.issn.2095-6134.2017.05.013
[1] Gingold R A, Monaghan J J. Smoothed particle hydrodynamics:theory and application to non-spherical stars[J]. Monthly Notices of the Royal Astronomical Society, 1977,181(3):375-389.
[2] Lucy L B. A numerical approach to the testing of the fission hypothesis[J]. The Astronomical Journal, 1977,82:1013-1024.
[3] Shao S, Lo E Y M. Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface[J]. Advances in Water Resources, 2003,26(7):787-800.
[4] Laigle D, Lachamp P, Naaim M. SPH-based numerical investigation of mudflow and other complex fluid flow interactions with structures[J]. Computational Geosciences, 2007,11(4):297-306.
[5] Manenti S, Sibilla S, Gallati M, et al. SPH Simulation of Sediment Flushing Induced by a Rapid Water Flow[J]. Journal of Hydraulic Engineering, 2012,138(3):272-284.
[6] Razavitoosi S L, Ayyoubzadeh S A, Valizadeh A. Two-phase SPH modelling of waves caused by dam break over a movable bed[J]. International Journal of Sediment Research, 2014,29(3):344-356.
[7] Ulrich C, Leonardi M, Rung T. Multi-physics SPH simulation of complex marine-engineering hydrodynamic problems[J]. Ocean Engineering, 2013,64:109-121.
[8] Ran Q, Tong J, Shao S, et al. Incompressible SPH scour model for movable bed dam break flows[J]. Advances in Water Resources, 2015,82(8):39-50.
[9] Shakibaeinia A, Jin Y-C. A mesh-free particle model for simulation of mobile-bed dam break[J]. Advances in Water Resources, 2011,34(6):794-807.
[10] Fourtakas G, Rogers B D. Modelling multi-phase liquid-sediment scour and resuspension induced by rapid flows using Smoothed Particle Hydrodynamics (SPH) accelerated with a Graphics Processing Unit (GPU)[J]. Advances in Water Resources, 2016,92(6):186-199.
[11] Xu X, Ouyang J, Yang B, et al. SPH simulations of three-dimensional non-Newtonian free surface flows[J]. Computer Methods in Applied Mechanics and Engineering, 2013,256(4):101-116.
[12] Fourtakas G, Rogers B D, Laurence D R. Modelling sediment resuspension in industrial tanks using SPH[J]. La Houille Blanche, 2013,(2):39-45.
[13] Monaghan J J. Simulating free surface flows with SPH[J]. Journal of Computational Physics, 1994,110(2):399-406.
[14] Morris J, Monaghan J. A switch to reduce SPH viscosity[J]. Journal of Computational Physics, 1997,136(1):41-50.
[15] Fang J, Parriaux A, Rentschler M, et al. Improved SPH methods for simulating free surface flows of viscous fluids[J]. Applied Numerical Mathematics, 2009,59(2):251-271.
[16] Chen W-F, Mizuno E. Nonlinear analysis in soil mechanics[M]. Amsterdam:Elsevier, 1990.
[17] Rodriguez-Paz M X, Bonet J. A corrected smooth particle hydrodynamics method for the simulation of debris flows[J]. Numerical Methods for Partial Differential Equations, 2004,20(1):140-163.
[18] Frigaard I A, Nouar C. On the usage of viscosity regularisation methods for visco-plastic fluid flow computation[J]. Journal of Non-Newtonian Fluid Mechanics, 2005,127(127):1-26.
[19] Papanastasiou T C. Flows of Materials with Yield[J]. Journal of Rheology, 1987,31(5):385-404.
[20] Gotoh H, Fredsoe Jr. Lagrangian two-phase flow model of the settling behavior of fine sediment dumped into water//International Conference on Coastal Engineering, 2001:3906-3919.
[21] Vand V. Viscosity of Solutions and Suspensions. I. Theory[J]. The Journal of Physical and Colloid Chemistry, 1948,52(2):277-299.
[22] Bagnold R A. Experiments on a Gravity-Free Dispersion of Large Solid Spheres in a Newtonian Fluid under Shear[J]. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences, 1954,225(1160):49-63.
[23] Armanini A, Larcher M, Nucci E, et al. Submerged granular channel flows driven by gravity[J]. Advances in Water Resources, 2014,63(2):1-10.
[24] Savage S B. The mechanics of rapid granular flows[J]. Advances in Applied Mechanics, 1984,24(87):289-366.
[25] Spinewine B. Two-layer flow behaviour and the effects of granular dilatancy in dam-break induced sheet-flow. Belgium:Université catholique de Louvain PhD Thesis, 2005.
[26] Leimkuhler B J, Reich S, Skeel R D. Mathematical approaches to biomolecular structure and dynamics[M]. New York:Springer,1996:161-185.
[27] Molteni D, Colagrossi A. A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH[J]. Computer Physics Communications, 2009,180(6):861-872.