0
Research Papers: Fundamental Issues and Canonical Flows

Simulation of Shallow Flows in Nonuniform Open Channels

[+] Author and Article Information
Qiuhua Liang

Lecturer in Hydraulic Engineering, School of Civil Engineering and Geosciences, Newcastle University, Newcastle Upon Tyne NE1 7RU, UKqiuhua.liang@ncl.ac.uk

J. Fluids Eng 130(1), 011205 (Jan 18, 2008) (9 pages) doi:10.1115/1.2829593 History: Received March 09, 2007; Revised August 20, 2007; Published January 18, 2008

This paper presents a new formulation of the 2D shallow water equations, based on which a numerical model (referred to as NewChan) is developed for simulating complex flows in nonuniform open channels. The new shallow water equations mathematically balance the flux and source terms and can be directly applied to predict flows over irregular bed topography without any necessity for a special numerical treatment of source terms. The balanced governing equations are solved on uniform Cartesian grids using a finite-volume Godunov-type scheme, enabling automatic capture of transcritical flows. A high-order numerical scheme is achieved using a second-order Runge–Kutta integration method. A very simple immersed boundary approach is used to deal with an irregular domain geometry. This method can be easily implemented in a Cartesian model and does not have any influence on computational efficiency. The numerical model is validated against several benchmark tests. The computed results are compared with analytical solutions, previously published predictions, and experimental measurements and excellent agreements are achieved.

Copyright © 2008 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 14

Dam break: experimental setup

Grahic Jump Location
Figure 15

Dam break: 3D surface elevation and depth contours at different output times. (a) t=4.0s and (b) t=7.0s.

Grahic Jump Location
Figure 1

Definition sketch of bed topography for the shallow water equations

Grahic Jump Location
Figure 2

Local boundary modification method for a Cartesian grid model. (a) Free surface elevation. (b) Velocity.

Grahic Jump Location
Figure 3

Tidal wave propagating in a channel with an irregular bed profile

Grahic Jump Location
Figure 4

Oblique hydraulic jump: sample computational grid

Grahic Jump Location
Figure 5

Oblique hydraulic jump: convergence history

Grahic Jump Location
Figure 6

Oblique hydraulic jump: 3D water surface predicted on a 160×120 grid

Grahic Jump Location
Figure 7

Oblique hydraulic jump: velocity vectors near the inclined wall. (a) 40×30 grid, (b) 80×60 grid, and (c) 160×120 grid.

Grahic Jump Location
Figure 8

Oblique hydraulic jump: depth contours and central water surface profiles on different grids

Grahic Jump Location
Figure 9

Oblique hydraulic jump: convergence history for the case without a boundary treatment

Grahic Jump Location
Figure 10

Oblique hydraulic jump: results without a boundary treatment

Grahic Jump Location
Figure 11

Oblique hydraulic jump: velocity vectors near the inclined wall without a boundary treatment

Grahic Jump Location
Figure 12

Hydraulic jump and drop: convergence history

Grahic Jump Location
Figure 13

Hydraulic jump and drop: surface profile

Grahic Jump Location
Figure 16

Dam break: comparison between the predicted time history of water surface elevation and experimental measurements at four gauge points. (a) Gauge 1. (b) Gauge 2. (c) Gauge 3. (d) Gauge 4.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In