A well-balanced solver for the Saint Venant equations with variable cross-section

Borsche, Raul

doi:10.1515/jnma-2015-0008

Cited by 2 publications

(2 citation statements)

References 29 publications

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“…For the Saint Venant equation, there exist many powerful solvers. Here, we use the augmented Riemann solver described in . It can accurately capture wet–dry interfaces and is well balanced with respect to the bottom slope and variations in the cross section.…”

Section: Methodsmentioning

confidence: 99%

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Flooding in urban drainage systems: coupling hyperbolic conservation laws for sewer systems and surface flow

Borsche

Klar

2014

Numerical Methods in Fluids

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Abstract. In this paper we propose a model for a sewer network coupled to surface flow and investigate it numerically. In particular, we present a new model for the manholes in storm sewer systems. It is derived using the balance of the total energy in the complete network. The resulting system of equations contains, aside from hyperbolic conservation laws for the sewer network and algebraic relations for the coupling conditions, a system of ODEs governing the flow in the manholes. The manholes provide natural points for the interaction of the sewer system and the run off on the urban surface modelled by shallow water equations. Finally, a numerical method for the coupled system is presented. In several numerical tests we study the influence of the manhole model on the sewer system and the coupling with 2D surface flow.

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Section: Methodsmentioning

confidence: 99%

“…For this, a huge variety of solvers have been developed (e.g., [40][41][42][43]). In the following, we use the augmented Riemann solver presented in [44,45], which is of the same type as the one for the conduits [29]. For all details of the 2D realization, we refer to these publications.…”

Section: The Surfacementioning

confidence: 99%