Verificação da solução das equações de Saint-Venant com base no método difusivo de lax para propagação de vazões em canais naturais

ABSTRACT

Hydrodynamic models, based on the Saint-Venant equations, represent the transient flow in water systems, and simulate flow routing over time and space. Several numerical solutions have been applied to these expressions, but often differences are found in results among distinct procedures, considering that all numerical approaches have limitations. Natural channels are characterized by a dynamic flow behavior, with multiple uses of water and changes in morphology, which occur naturally and by human influence. In this context, this study seeks to complement the understanding of different assumptions and approximations for solution of the Saint-Venant equations, verifying results of the Lax diffusive scheme and comparing with HEC-RAS model. The case study consists of a river that covers an urban area (River Iguaçu, located in Curitiba, Paraná). Comparing the observed and simulated hydrographs, it was possible to assess that how the equations are solved, which determines the type of boundary conditions to be used, that may contribute to differences in simulated flows. Additionally, the calibration strategy and the hypothesis of trapezoidal cross-sections produced positive results. The development of this research should also encourage the progress in solving the hydrodynamic model trough the Lax diffusive scheme, particularly concerning computational efficiency. Explicit schemes, although more sensitive to the time step, have the advantage of simplicity to implement, which could be beneficial in the study of complex systems such as urban rivers.

Keywords:
Saint-Venant equations; Lax diffusive scheme; HEC-RAS; Iguaçu River