In another study, Rajar (1978) studied a one-dimensional flood wave propagation from an earthen dam failure. His model solves the St. Venant equations by means of either a first-order diffusive or a second-order Lax-Wendroff numerical scheme. A review of the literature indicates that the most frequently used numerical scheme is the method of characteristics (to solve the governing flow equations) such as described in Sakkas and Strelkoff (1973), Chen (1980), and Chen and Armbruster (1980).
Although many dam-break studies involve flood flow regimes which are truly two-dimensional (in the horizontal plane), the two dimensional case has not received much attention in the literature. Katopodes and Strelkoff (1978) use the method of bicharacteristics to solve the governing equations of continuity and momentum. The model utilizes a moving grid algorithm to follow the flood wave propagation, and also employs several interpolation schemes to approximate the nonlinearity effects. In a much simpler approach, Xanthopoulos and Koutitas (1976) use a diffusion model (i.e. the inertia terms are assumed negligible in comparison to the pressure, friction, and gravity components) to approximate a two-dimensional flow field. The model assumes that the flow regime in the flood plain is such that the inertia terms (local and convective acceleration) are negligible. In a one-dimensional model, Akan and Yen (1981) also use the diffusion approach to model hydrograph confluences at channel junctions. In the latter study, comparisons of modeling results were made between the diffusion model, a complete dynamic wave model solving the total equation system, and the basic kinematic wave equation model (that is, the inertia and pressure terms are assumed negligible in comparison to the friction and gravity terms). The differences between the diffusion model and the dynamic wave model were small, showing only minor discrepancies.
|
|