Hostname: page-component-7b7567c8c-wxvwp Total loading time: 0 Render date: 2026-11-15T05:56:26.451Z Has data issue: false hasContentIssue false
  • English
  • Français

A High-Order Numerical Method to Study Three-Dimensional Hydrodynamics in a Natural River

Published online by Cambridge University Press:  23 March 2015

Luyu Shen,
Changgen Lu,
Weiguo Wu and
Shifeng Xue
Luyu Shen
Affiliation:
College of Marine Sciences, Nanjing University of Information Science and Technology, Nanjing 210044, ChinaCollege of Atmospheric Sciences, Nanjing University of Information Science and Technology, Nanjing 210044, China
Changgen Lu*
Affiliation:
College of Marine Sciences, Nanjing University of Information Science and Technology, Nanjing 210044, China
Weiguo Wu
Affiliation:
Department of Engineering Mechanics, China University of Petroleum, Dongying 266555, China
Shifeng Xue
Affiliation:
Department of Engineering Mechanics, China University of Petroleum, Dongying 266555, China
*
*Corresponding author. Email: shenluyu99@foxmail.com (L. Shen), cglu@nuist.edu.cn (C. Lu), mailtowwg@gmail.com (W. Wu), xuesf@126.com (S. Xue)

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

A high-order numerical method for three-dimensional hydrodynamics is presented. The present method applies high-order compact schemes in space and a Runge-Kutta scheme in time to solve the Reynolds-averaged Navier-Stokes equations with the k-ε turbulence model in an orthogonal curvilinear coordinate system. In addition, a two-dimensional equation is derived from the depth-averaged momentum equations to predict the water level. The proposed method is first validated by its application to simulate flow in a 180° curved laboratory flume. It is found that the simulated results agree with measurements and are better than those from SIMPLEC algorithm. Then the method is applied to study three-dimensional hydrodynamics in a natural river, and the simulated results are in accordance with measurements.

Keywords

65M0676F6035Q35Compact schemethree-dimensional hydrodynamicsk-ε turbulence modelorthogonal curvilinear coordinate systemRunge-Kutta scheme

Information

Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 2 , April 2015, pp. 180 - 195
Copyright
Copyright © Global-Science Press 2015 

References

[1]Papanicolaou, A. N., Elhakeem, M. and Krallis, G.et al., Sediment transport modeling review-current and future developments, J. Hydraul. Eng., 134 (2008), pp. 1–14.CrossRefGoogle Scholar
[2]Demuren, A. O. and Rodi, W., Calculation of flow and pollutant dispersion in meandering channels, J. Fluid. Mech., 172 (1986), pp. 63–92.CrossRefGoogle Scholar
[3]Ye, J. and Mccorquodale, J. A., Simulation of curved open channel flows by 3D hydrodynamic model, J. Hydraul. Eng., 124 (1998), pp. 687–698.CrossRefGoogle Scholar
[4]Wu, W., Rodi, W. and Wenka, T., 3D numerical modeling of flow and sediment transport in open channels, J. Hydraul. Eng., 126 (2000), pp. 4–15.CrossRefGoogle Scholar
[5]Rüther, N. and Olsen, N. R., Three-dimensional modeling of sediment transport in a narrow 90? channel bend, J. Hydraul. Eng., 131 (2005), pp. 917–920.CrossRefGoogle Scholar
[6]Zhang, M. L. and Shen, Y. M., Application of 3-D RNG k-ε turbulence model of meandering river, J. Hydroelec. Eng., 26 (2007), pp. 86–91 (in Chinese).Google Scholar
[7]Khosronejad, A., Rennie, C. D. and Salehi Neyshabouri, S. A. A.et al., 3D numerical modeling of flow and sediment transport in laboratory channel bends, J. Hydraul. Eng., 133 (2007), pp. 1123–1134.CrossRefGoogle Scholar
[8]Feurich, R. and Olsen, N. R. B., Three-dimensional modeling of nonuniform sediment transport in an S-shaped channel, J. Hydraul. Eng., 137 (2011), pp.495–495.CrossRefGoogle Scholar
[9]Zeng, J., Constantinescu, G. and Weber, L., A 3D non-hydrostatic model to predict flow and sediment transport in loose-bed channel bends, J. Hydraul. Res., 46 (2008), pp. 356–372.CrossRefGoogle Scholar
[10]Lele, S. K., Compact finite difference schemes with spectral-like resolution, J. Comput. Phys., 103 (1992), pp. 16–42.CrossRefGoogle Scholar
[11]Pereira, J. M. C., Kobayashi, M. H. and Pereira, J. C. F., A fourth-order-accurate finite volume compact method for the incompressible Navier-Stokes solutions, J. Comput. Phys., 167 (2001), pp. 217–243.CrossRefGoogle Scholar
[12]Hokpunna, A. and Manhart, M., Compact fourth-order finite volume method for numerical solutions of Navier-Stokes equations on staggered grids, J. Comput. Phys., 229 (2010), pp. 7545–7570.CrossRefGoogle Scholar
[13]Elhami, A. A., Kazemzadeh, H. S. and Mashayek, F., Evaluation of a fourth-order finite-volume compact scheme for LES with explicit filtering, Numer. Heat. Tr. B-Fund., 48 (2005), pp. 147–163.CrossRefGoogle Scholar
[14]Nagarajan, S., Lele, S. K. and Ferziger, J. H., A robust high-order compact method for large eddy simulation, J. Comput. Phys., 191 (2003), pp. 392–419.CrossRefGoogle Scholar
[15]Fu, D. and Ma, Y., A high order accurate difference scheme for complex flow fields, J. Comput. Phys., 134 (1997), PP. 1–15.CrossRefGoogle Scholar
[16]De Vriend, H. J., A mathematical model of steady flow in curved shallow channels, J. Hydraul. Res., 15 (1977), pp. 37–54.CrossRefGoogle Scholar
[17]Noat, D., Response of channel flow to roughness heterogeneity, J. Hydraul. Eng., 110 (1984), pp. 1568–1587.CrossRefGoogle Scholar
[18]Lu, C., Cao, W. and Zhang, Y.et al., Large eddies induced by local impulse at wall of boundary layer with pressure gradients, Prog. Nat. Sci., 18 (2008), pp. 873–878.CrossRefGoogle Scholar
[19]Harlow, F. H. and Welch, J. E., Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids., 8 (1965), pp. 2182.CrossRefGoogle Scholar