Comptes Rendus
no. 7
Physical based numerical schemes for the discretization of the sediment settling term
Xinhua Lu1, 2  ; Xiaofeng Zhang1 ; Bingjiang Dong3 ; Huaihan Liu2 ; Bing Mao4
1 State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
2 Changjiang Waterway Planning, Design and Research Institute, Wuhan 430010, China
3 Yangtze River Scientific Research Institute, Wuhan 430015, China
4 Hydrology Bureau, Yangtze River Water Resource Commission, Wuhan 430010, China
Comptes Rendus. Mécanique, Volume 341 (2013) no. 7, pp. 581-591.

In this paper, the discretization of the sediment settling term is investigated. Two potential problems induced by the incorrect discretization of this term are analyzed. It shows that even the first-order upwind algorithm, the most stable and conservative scheme, cannot always ensure stability and mass conservation. To tackle these issues, three rules are proposed. Based on these rules, two schemes are designed. The performances of different schemes are tested in a study of sediment motions under a wave-breaking situation. The results show that the unphysical problems are relieved or totally avoided by the new schemes.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2013.05.002
Mots clés : Sedimentation, Suspension, Mass conservation, Wave breaking, Settling velocity

Xinhua Lu 1, 2 ; Xiaofeng Zhang 1 ; Bingjiang Dong 3 ; Huaihan Liu 2 ; Bing Mao 4

1 State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
2 Changjiang Waterway Planning, Design and Research Institute, Wuhan 430010, China
3 Yangtze River Scientific Research Institute, Wuhan 430015, China
4 Hydrology Bureau, Yangtze River Water Resource Commission, Wuhan 430010, China 
@article{CRMECA_2013__341_7_581_0,
     author = {Xinhua Lu and Xiaofeng Zhang and Bingjiang Dong and Huaihan Liu and Bing Mao},
     title = {Physical based numerical schemes for the discretization of the sediment settling term},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {581--591},
     publisher = {Elsevier},
     volume = {341},
     number = {7},
     year = {2013},
     doi = {10.1016/j.crme.2013.05.002},
     language = {en},
}
TY  - JOUR
AU  - Xinhua Lu
AU  - Xiaofeng Zhang
AU  - Bingjiang Dong
AU  - Huaihan Liu
AU  - Bing Mao
TI  - Physical based numerical schemes for the discretization of the sediment settling term
JO  - Comptes Rendus. Mécanique
PY  - 2013
SP  - 581
EP  - 591
VL  - 341
IS  - 7
PB  - Elsevier
DO  - 10.1016/j.crme.2013.05.002
LA  - en
ID  - CRMECA_2013__341_7_581_0
ER  - 
%0 Journal Article
%A Xinhua Lu
%A Xiaofeng Zhang
%A Bingjiang Dong
%A Huaihan Liu
%A Bing Mao
%T Physical based numerical schemes for the discretization of the sediment settling term
%J Comptes Rendus. Mécanique
%D 2013
%P 581-591
%V 341
%N 7
%I Elsevier
%R 10.1016/j.crme.2013.05.002
%G en
%F CRMECA_2013__341_7_581_0
Xinhua Lu; Xiaofeng Zhang; Bingjiang Dong; Huaihan Liu; Bing Mao. Physical based numerical schemes for the discretization of the sediment settling term. Comptes Rendus. Mécanique, Volume 341 (2013) no. 7, pp. 581-591. doi : 10.1016/j.crme.2013.05.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.05.002/

[1] É. Guazzelli Sedimentation of small particles: how can such a simple problem be so difficult?, C. R. Mecanique, Volume 334 (2006), pp. 539-544

[2] D. Gonzalez-Rodriguez; O.S. Madsen Boundary-layer hydrodynamics and bedload sediment transport in oscillating water tunnels, J. Fluid Mech., Volume 667 (2010), pp. 4-84

[3] C.M. Fang; Q.W. Han; M.M. He Analysis on plunging conditions of density stratified flow and 2-D simulation, J. Sediment. Res., Volume 4 (1997), pp. 68-75 (in Chinese)

[4] Y. Peng; Y.T. Li; W.X. Huai 2D vertical numerical solution to the density current plunge flow, J. Sediment. Res., Volume 6 (2000), pp. 25-30 (in Chinese)

[5] H.W. Fang; W. Rodi Three-dimensional calculations of flow and suspended sediment transport in the neighborhood of the dam for the Three Gorges Project (TGP) reservoir in the Yangtze River, J. Hydraul. Res., Volume 41 (2003) no. 4, pp. 379-394

[6] Y.J. Chou; O.B. Fringer Modeling dilute sediment suspension using large-eddy simulation with a dynamic mixed model, Phys. Fluids, Volume 20 (2008), p. 115103 (13 pp)

[7] C.E. Ozdemir; T.J. Hsu; S. Balachandar Simulation of fine sediment transport in oscillatory boundary layer, J. Hydro-Environ. Res., Volume 3 (2010) no. 4, pp. 247-259

[8] B.C. Liang; H.J. Li; D.Y. Lee Numerical study of three-dimensional suspended sediment transport in waves and currents, Ocean Eng., Volume 34 (2007) no. 11, pp. 1569-1583

[9] J.C. Warner; C.R. Sherwood; R.P. Signell et al. Development of a three-dimensional, regional, coupled wave, current, and sediment-transport model, Comput. Geosci., Volume 34 (2008), pp. 1284-1306

[10] T. Suzuki; A. Okayasu; T. Shibayama A numerical study of intermittent sediment concentration under breaking waves in the surf zone, Coastal Eng., Volume 54 (2007) no. 5, pp. 433-444

[11] E.A. Zedler; R.L. Street Sediment transport over ripples in oscillatory flow, J. Hydraul. Eng., Volume 132 (2006) no. 2, pp. 180-193

[12] R. Zhang; J. Xie Sedimentation Research in China: Systematic Selections, China Water and Power Press, Beijing, 1993

[13] V. Yakhot; S.A. Orszag Renormalization group analysis of turbulence I. Basic theory, J. Sci. Comput., Volume 1 (1986) no. 1, pp. 3-51

[14] Y. Hu; G. Xin; X.H. Lu; R.R. Dalrymple; L. Shen Idealized numerical simulation of breaking water wave propagating over a viscous mud layer, Phys. Fluids, Volume 24 (2012), p. 112104 (20 pp)

[15] F.H. Harlow; J.E. Welch Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids, Volume 8 (1965), pp. 2182-2189

[16] J. Zhu A low-diffusive and oscillation-free convection scheme, Commun. Appl. Numer. Methods, Volume 7 (1991), pp. 225-232

[17] J. Kim; P. Moin Application of a fractional-step method to incompressible Navier–Stokes equations, J. Comput. Phys., Volume 323 (1985), pp. 308-323

[18] H.A. van de Vorst Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Comput., Volume 13 (1992) no. 2, pp. 631-644

[19] Y.J. Chou; O.B. Fringer A model for the simulation of coupled flow-bed form evolution in turbulent flows, J. Geophys. Res., Volume 115 (2010) no. C10041, pp. 1-20

[20] L. Amoudry; T.J. Hsu; P.L.F. Liu Schmidt number and near-bed boundary condition effects on a two-phase dilute sediment transport model, J. Geophys. Res., Volume 110 (2005) no. C09003, pp. 1-12

[21] X. Yu; T.J. Hsu; D.M. Hanes Sediment transport under wave groups: Relative importance between nonlinear waveshape and nonlinear boundary layer streaming, J. Geophys. Res., Volume 115 (2010) no. C02013, pp. 1-18

[22] P. Nielsen Coastal Bottom Boundary Layers and Sediment Transport, World Scientific, Singapore, 1992

[23] H. Kim Temporal variation of suspended sediment concentration for waves over ripples, Int. J. Sediment. Res., Volume 18 (2003) no. 3, pp. 248-265

[24] E.A. Zedler; R.L. Street Large-eddy simulation of sediment transport: currents over ripples, J. Hydraul. Eng., Volume 127 (2001) no. 6, pp. 444-452

[25] Y.C. Bai; C.O. Ng Large eddy simulation for plunge breaker and sediment suspension, China Ocean Eng., Volume 16 (2002) no. 2, pp. 151-164

[26] M. Sussman; E.G. Puckett A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows, J. Comput. Phys., Volume 162 (2000), pp. 301-337

[27] D.L. Sun; W.Q. Tao A coupled volume-of-fluid and level set (VOSET) method for computing incompressible two-phase flows, Int. J. Heat Mass Transfer, Volume 53 (2010) no. 4, pp. 645-655

[28] P. Lubin; S. Vincent; S. Abadie; J.P. Caltagirone Three-dimensional large eddy simulation of air entrainment under plunging breaking waves, Coastal Eng., Volume 53 (2006), pp. 631-655

Cité par Sources :

Commentaires - Politique