A finite difference lattice Boltzmann method (FDLBM) for the simulation of mud and debris flows for one-dimensional cases has been introduced. The proposed FDLBM recovers the generalized equations of mud and debris flows, that is, an unsteady one-dimensional Saint-Venant equation, including the effects of the non-Newtonian behavior of the mixture of water and soil, contraction–expansion losses (or large eddy loss), wind force, various geometries, and lateral inflow or outflow. The proposed FDLBM can be implemented for various non-Newtonian viscoplastic constitutive models of the studied mud and debris flows. The method is validated against previous studies for several benchmark cases, including steady-state problems, hydraulic jump tests, dam breaks with dry and wet beds, and slope dam break floods. Finally, the Anhui debris dam failure flood was investigated by this approach, and the results demonstrated a good agreement with the observed computational and field tests.
References
1.
G.
Han
and D.
Wang
, “Numerical modeling of Anhui debris flow
,” J. Hydraul. Eng. ASCE
122
, 262
–265
(1996
).2.
G.
Benito
, T.
Grodek
, and Y.
Enzel
, “The geomorphic and hydrologic impacts of the catastrophic failure of flood-control-dams during the 1996-Biescas flood (Central Pyrenees, Spain)
,” Z. Geomorphol.
42
, 417
–437
(1998
).3.
X.
Fan
, C. X.
Tang
, C. J.
Van Westen
, and D.
Alkema
, “Simulating dam-break flood scenarios of the Tangjiashan landslide dam induced by the Wenchuan Earthquake
,” Nat. Hazards Earth Syst. Sci.
12
, 3031
–3044
(2012
).4.
G. L.
Wang
, “Lessons learned from protective measures associated with the 2010 Zhouqu debris flow disaster in China
,” Nat. Hazards
69
, 1835
–1847
(2013
).5.
X.
Chen
, P.
Cui
, Y.
You
, J.
Chen
, and D.
Li
, “Engineering measures for debris flow hazard mitigation in the Wenchuan earthquake area
,” Eng. Geol.
194
, 73
–85
(2015
).6.
P. C.
Larraui
and U.
Lall
, “Tailings dams failures: Updated statistical model for discharge volume and runout
,” Environments
5
, 28
(2018
).7.
S.
Cucchiaro
, M.
Cavalli
, D.
Vericat
, S.
Crema
, M.
Llena
, A.
Beinat
, L.
Marchi
, and F.
Cazorzi
, “Geomorphic effectiveness of check dams in a debris-flow catchment using multi-temporal topographic surveys
,” Catena
174
, 73
–83
(2019
).8.
T.
Baggio
and V.
D'Agostino
, “Simulating the effect of check dam collapse in a debris-flow channel
,” Sci. Total Environ.
816
, 151660
(2022
).9.
10.
H.
Chanson
, The Hydraulics of Open Channel Flow: An Introduction
, 2nd ed. (Elsevier
, 2004
), pp. 339
–347
.11.
J. A.
Cunge
, F. M.
Holly
, and A.
Verwey
, Practical Aspects of Computational River Hydraulics
(Pitman Publishing Ltd
., Boston, MA
, 1980
).12.
B. R.
Hodges
, “Conservative finite-volume forms of the Saint-Venant equations for hydrology and urban drainage
,” Hydrol. Earth Syst. Sci.
23
, 1281
–1304
(2019
).13.
R.
Moussa
and C.
Bocquillon
, “Criteria for the choice of flood-routing methods in natural channels
,” J. Hydrol.
186
, 1
–30
(1996
).14.
A.
Bermudez
, A.
Dervieux
, J. A.
Desideri
, and M. E.
Vazquez
, “Upwind schemes for the two-dimensional shallow water equations with variable depth using unstructured meshes
,” Comput. Methods Appl. Mech. Eng.
155
, 49
–72
(1998
).15.
G.
Kesserwani
, R.
Ghostine
, J.
Vazquez
, A.
Ghenaim
, and R.
Mose
, “Application of a second-order Runge–Kutta discontinuous Galerkin scheme for the shallow water equations with source terms
,” Int. J. Numer. Methods Fluids
56
, 805
–821
(2008
).16.
P. J.
Dellar
, “Non-hydrodynamic modes and a priori construction of shallow water lattice Boltzmann equations
,” Phys. Rev. E
65
, 036309
(2002
).17.
J. G.
Zhou
, “A lattice Boltzmann model for the shallow water equations
,” Comput. Methods Appl. Mech. Eng.
191
, 3527
–3539
(2002
).18.
J. G.
Zhou
, Lattice Boltzmann Methods for Shallow Water Flows
(Springer
, New York
, 2004
).19.
G.
Thommes
, M.
Seaid
, and M. K.
Banda
, “Lattice Boltzmann methods for shallow water flow applications
,” Int. J. Numer. Methods Fluids
55
, 673
–692
(2007
).20.
P.
van Thang
, B.
Chopard
, L.
Lefèvre
, D. A.
Ondo
, and E.
Mendes
, “Study of the 1D lattice Boltzmann shallow water equation and its coupling to build a canal network
,” J. Comput. Phys.
229
, 7373
–7400
(2010
).21.
J. G.
Zhou
, “Enhancement of the LABSWE for shallow water flows
,” J. Comput. Phys.
230
, 394
–401
(2011
).22.
J. G.
Zhou
and H.
Liu
, “Determination of bed elevation in the enhanced lattice Boltzmann method for the shallow-water equations
,” Phys. Rev. E
88
, 023302
(2013
).23.
H.
Liu
, H.
Wang
, S.
Liu
, C.
Hu
, Y.
Ding
, and J.
Zhang
, “Lattice Boltzmann method for the Saint–Venant equations
,” J. Hydrol.
524
, 411
–416
(2015
).24.
A.
De Rosis
, “A central moments-based lattice Boltzmann scheme for shallow water equations
,” Comput. Methods Appl. Mech. Eng.
319
, 379
–392
(2017
).25.
S.
Ožvat
and L.
Budinski
, “Non-uniform grid based LBM for the Saint-Venant equations
,” J. Hydrol.
563
, 435
–445
(2018
).26.
Z.
Yang
, F.
Bai
, and K.
Xiang
, “A lattice Boltzmann model for the open channel flows described by the Saint-Venant equations
,” R. Soc. Open Sci.
6
, 190439
(2019
).27.
Y.
Liu
, Z.
Chai
, X.
Guo
, and B.
Shi
, “A lattice Boltzmann model for the viscous shallow water equations with source terms
,” J. Hydrol.
598
, 126428
(2021
).28.
D.
Stipic
, L.
Budinski
, and J.
Fabian
, “Sediment transport and morphological changes in shallow flows modelled with the lattice Boltzmann method
,” J. Hydrol.
606
, 127472
(2022
).29.
M.
Jin
and D. L.
Fread
, “1D modeling of mud/debris unsteady flows
,” J. Hydraul. Eng. ASCE
125
, 827
–834
(1999
).30.
Hydrologic Engineering Center-River Analysis System (HEC-RAS, 5.0.6) documentations, Mud and Debris flow, Non-Newtonian Flow equations, 1D Saint-Venant Equations.
31.
S. C.
Fu
and R. M. C.
So
, “Modeled lattice Boltzmann equation and the constant-density assumption
,” AIAA J.
47
, 3038
–3042
(2009
).32.
S. C.
Fu
, W. W. F.
Leung
, and R. M. C.
So
, “A lattice Boltzmann method based numerical scheme for microchannel flows
,” J. Fluids Eng.
31
, 081401
(2009
).33.
S. C.
Fu
, R. M. C.
So
, and W. W. F.
Leung
, “Linearized Boltzmann type equation based finite difference method for incompressible flow
,” Comput. Fluids
69
, 67
–80
(2012
).34.
R. M. C.
So
, R. C. K.
Leung
, E. W. S.
Kam
, and S. C.
Fu
, “Progress in the development of a new lattice Boltzmann method
,” Comput. Fluids
190
, 440
(2019
).35.
G. H. R.
Kefayati
, “An immersed boundary-lattice Boltzmann method for thermal and thermo-solutal problems of Newtonian and non-Newtonian fluids
,” Phys. Fluids
32
, 073103
(2020
).36.
G. H. R.
Kefayati
, “Lattice Boltzmann simulation of double-diffusive natural convection of viscoplastic fluids in a porous cavity
,” Phys. Fluids
31
, 013105
(2019
).37.
R. R.
Huilgol
and G. H. R.
Kefayati
, “From mesoscopic models to continuum mechanics: Newtonian and non-Newtonian fluids
,” J. Non-Newtonian Fluid Mech.
233
, 146
–154
(2016
).38.
R. R.
Huilgol
and G. H. R.
Kefayati
, “A particle distribution function approach to the equations of continuum mechanics in Cartesian, cylindrical and spherical coordinates: Newtonian and non-Newtonian fluids
,” J. Non-Newtonian Fluid Mech.
251
, 119
–131
(2018
).39.
R.
LeVeque
, “Finite volume methods for hyperbolic problems
,” Cambridge Texts in Applied Mathematics
(Cambridge University Press
, 2004
).40.
E. F.
Toro
, Shock-Capturing Methods for Free-Surface Shallow Flows
(Wiley
, New York
, 2001
).41.
E. F.
Toro
and A.
Siviglia
, “PRICE: Primitive centered schemes for hyperbolic systems
,” Int. J. Numer. Methods Fluids
42
, 1263
–1291
(2003
).42.
X.
Ying
, A. A.
Khan
, and S. Y.
Wang
, “Upwind conservative scheme for the Saint Venant equations
,” J. Hydraul. Eng. ASCE
130
, 977
–987
(2004
).43.
M.
Catella
, E.
Paris
, and L.
Solari
, “Conservative scheme for numerical modeling of flow in natural geometry
,” J. Hydraul. Eng. ASCE
134
, 736
–748
(2008
).44.
T. J.
Chang
, H. M.
Kao
, K. H.
Chang
, and M. H.
Hsu
, “Numerical simulation of shallow-water dam break flows in open channels using smoothed particle hydrodynamics
,” J. Hydrol.
408
, 78
–90
(2011
).45.
B.
Wang
, Y.
Chen
, Y.
Peng
, J.
Zhang
, and Y.
Guo
, “Analytical solution of shallow water equations for ideal dam-break flood along a wet-bed slope
,” J. Hydraul. Eng. ASCE
146
, 06019020
(2020
).46.
G. H. R.
Kefayati
, “FDLBM simulation of entropy generation in double diffusive natural convection of power-law fluids in an enclosure with Soret and Dufour effects
,” Int. J. Heat Mass Transfer
89
, 267
–290
(2015
).47.
G. H. R.
Kefayati
and H.
Tang
, “Double-diffusive natural convection and entropy generation of Carreau fluid in a heated enclosure with an inner circular cold cylinder. I. Heat and mass transfer
,” Int. J. Heat Mass Transfer
120
, 731
–750
(2018
).48.
G. H. R.
Kefayati
and H.
Tang
, “Three-dimensional lattice Boltzmann simulation on thermosolutal convection and entropy generation of Carreau-Yasuda fluids
,” Int. J. Heat Mass Transfer
131
, 346
–364
(2019
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
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