Numerical Simulation of Shallow Water Flows Using Planar 2-D Algebraic-Stress Model in Curvilinear Coordinates
by
S M Wong
The Open University of Hong Kong
Coauthors: T S Li, X G Wu, Y M Shen

In this paper we introduce a stable and effective computational scheme using planar 2-D algebraic-stress model for simulating the shallow water flows. The mathematical models involved are the set of two-dimensional conservation equations for momentum and mass. The governing equations are transformed into curvilinear coordinates. The space discretization in the horizontal directions is formulated through the Arakawa B-staggered grid system; such staggered grid can reduce the difficulty of computations. Water level scanning method incorporated with the wall-function is used to treat the moving boundary. In addition to the study of the turbulence model, the effects of Reynolds-stress are investigated. An algebraic Reynolds stress model is developed using k-ε double equations in non-orthogonal curvilinear coordinates, the numerical results are compared with that of the standard k-ε model. The proposed model is solved using the SIMPLEC algorithm and validated against the experimental data of meandering channel. The comparison shows that the proposed model is effective in predicting the velocity flow fields. The simulated result is very satisfactory in the sense that the flow pattern provides a strong agreement with the experimental data. This model is particularly appropriate for the problems of two-dimensional shallow-water equations and is important for the construction of hydraulic engineering.

Date received: March 28, 2007