In this paper we analyze the Hirano active layer model used in mixed sediment river morphodynamics concerning its ill-posedness. Ill-posedness causes the solution to be unstable to short-wave perturbations. This implies that the solution presents spurious oscillations, the amplitude of which depends on the domain discretization. Ill-posedness not only produces physically unrealistic results but may also cause failure of numerical simulations. By considering a two-fraction sediment mixture we obtain analytical expressions for the mathematical characterization of the model. Using these we show that the ill-posed domain is larger than what was found in previous analyses, not only comprising cases of bed degradation into a substrate finer than the active layer but also in aggradational cases. Furthermore, by analyzing a three-fraction model we observe ill-posedness under conditions of bed degradation into a coarse substrate. We observe that oscillations in the numerical solution of ill-posed simulations grow until the model becomes well-posed, as the spurious mixing of the active layer sediment and substrate sediment acts as a regularization mechanism. Finally we conduct an eigenstructure analysis of a simplified vertically continuous model for mixed sediment for which we show that ill-posedness occurs in a wider range of conditions than the active layer model.

Ill-posedness in modeling mixed sediment river morphodynamics / Chavarrias, V.; Stecca, G.; Blom, A.. - In: ADVANCES IN WATER RESOURCES. - ISSN 0309-1708. - ELETTRONICO. - 114:(2018), pp. 219-235. [10.1016/j.advwatres.2018.02.011]

Ill-posedness in modeling mixed sediment river morphodynamics

Stecca G.;
2018

Abstract

In this paper we analyze the Hirano active layer model used in mixed sediment river morphodynamics concerning its ill-posedness. Ill-posedness causes the solution to be unstable to short-wave perturbations. This implies that the solution presents spurious oscillations, the amplitude of which depends on the domain discretization. Ill-posedness not only produces physically unrealistic results but may also cause failure of numerical simulations. By considering a two-fraction sediment mixture we obtain analytical expressions for the mathematical characterization of the model. Using these we show that the ill-posed domain is larger than what was found in previous analyses, not only comprising cases of bed degradation into a substrate finer than the active layer but also in aggradational cases. Furthermore, by analyzing a three-fraction model we observe ill-posedness under conditions of bed degradation into a coarse substrate. We observe that oscillations in the numerical solution of ill-posed simulations grow until the model becomes well-posed, as the spurious mixing of the active layer sediment and substrate sediment acts as a regularization mechanism. Finally we conduct an eigenstructure analysis of a simplified vertically continuous model for mixed sediment for which we show that ill-posedness occurs in a wider range of conditions than the active layer model.
Chavarrias, V.; Stecca, G.; Blom, A.
Ill-posedness in modeling mixed sediment river morphodynamics / Chavarrias, V.; Stecca, G.; Blom, A.. - In: ADVANCES IN WATER RESOURCES. - ISSN 0309-1708. - ELETTRONICO. - 114:(2018), pp. 219-235. [10.1016/j.advwatres.2018.02.011]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/248685
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