Verification of Saint-Venant equations solution based on the lax diffusive method for flow routing in natural channels

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. RESUMOModelos hidrodinâmicos, formados pelas equações de Saint-Venant, representam o escoamento transitório em sistemas hídricos, e simulam a propagação de vazões ao longo do tempo e do espaço. Diversas soluções numéricas têm sido aplicadas a essas expressões, porém frequentemente são encontradas diferenças de resultados entre procedimentos, uma vez que toda aproximação numérica possui limitações. Canais naturais são caracterizados por um comportamento dinâmico das vazões, considerando os usos múltiplos da água e as alterações de morfologia, que ocorrem naturalmente ou por influência antrópica. Nesse contexto, esse trabalho procura complementar o entendimento acerca de diferentes hipóteses e aproximações para solução das equações de Saint-Venant, verificando resultados do esquema difusivo de Lax e comparando com o software HEC-RAS. O estudo de caso consiste em um rio que drena uma área densamente povoada (rio Iguaçu, localizado em Curitiba-PR). Ao comparar os hidrogramas observados e simulados, foi possível avaliar que a forma como as equações são resolvidas, que por sua vez determina o tipo de condição de contorno a ser utilizada, pode contribuir para diferenças na vazão simulada. Adicionalmente, foi observado que a calibração alcançada é adequada, assim como a hipótese de seção transversal trapezoidal. O desenvolvimento da pesquisa deve auxiliar ainda o avanço na solução do modelo hidrodi...

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