From the above conclusions, use of the diffusion approach, equation 22, in a two-dimensional DHM may be justified due to the low variation in predicted flooding depths (one-dimensional) with the exclusion of the inertia terms. Generally speaking, a two-dimensional model would be employed when the expansion nature of flood flows is anticipated. Otherwise, one of the available one-dimensional models would suffice for the analysis.
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Two-Dimensional Analysis
Introduction
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In this section, a two-dimensional DHM is developed. The model is based on a diffusion approach where gravity, friction, and pressure forces are assumed to dominate the flow equations. Such an approach has been used earlier by Xanthopoulos and Koutitas (1976) in the prediction of dam-break flood plains in Greece. In those studies, good results were also obtained by using the two-dimensional model for predicting one-dimensional flow quantities. In the preceding section a one-dimensional diffusion model has been considered and it has been concluded that for most velocity flow regimes (such as Fronde Number less than approximately 4), the diffusion model is a reasonable approximation of the full dynamic wave formulation.
An integrated finite difference grid model is developed which equates each cell-centered node to a function of the four neighboring cell nodal points. To demonstrate the predictive capacity of the flood plain model, a study of a hypothetical dam-break of the Crowley Lake dam near the City of Bishop, California (figure 7) is considered (Hromadka, et al., 1985).
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