Velocity-Depth Coupling in Shallow-Water Flows

Abstract

The two-dimensional shallow-water flow equations are first written in strong conservation form and are used for developing the flow model. In the discretization equations, based on the control volume method, the velocity field is found to be proportional to both the square of the depth and the depth itself. Due to this, none of the existing SIMPLE-like algorithms can be used to deal with the velocity-depth coupling. In this paper, the problem of velocity-depth coupling is studied, and a modified SIMPLE-like algorithm is described to treat it. Several applications of the model have shown that the method is efficient, simple, and has good convergence behavior. Also, a different value for the relaxation factor for depth is found to speed the convergence rate after stable convergence occurs. The results are in good agreement with both experimental observations and theoretical analysis. The method can straightforwardly be extended into unsteady shallow-water flows.