Abstract
Free-surface, two-phase flows constituted by water and a significant concentration of sediments (i.e. hyperconcentrated flows), are often studied under the classical 1D shallow-water assumptions. This paper deals with the problem of the numerical simulation of this type of flows in presence of a geometrical source term caused by a discontinuity in the bed. Since we work in the framework of the finite-volume Godunov-type numerical schemes, we focus on the exact and approximated solution to Riemann Problems at cell interfaces with a step-like bed discontinuity. The paper has a twofold aim. First, it provides insights into the properties of the Step Riemann Problems (SRPs), highlighting in particular that a contact wave with special features may develop. Second, it presents a two-step predictor-corrector algorithm for the solution of the SRPs. In the predictor step, a Generalized Roe solver is used in order to provide an estimation of the wave structure arising from the cell-interface, while in the corrector step the exact SRP is solved by means of an efficient iterative procedure. The capabilities of the proposed solver are tested by comparing numerical and exact solutions of some SRPs.
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Begnudelli, L., Rosatti, G. Hyperconcentrated 1D Shallow Flows on Fixed Bed with Geometrical Source Term Due to a Bottom Step. J Sci Comput 48, 319–332 (2011). https://doi.org/10.1007/s10915-010-9457-z
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DOI: https://doi.org/10.1007/s10915-010-9457-z