TY - JOUR
T1 - Ill-posedness in modeling mixed sediment river morphodynamics
AU - Chavarrias Borras, V.
AU - Stecca, Guglielmo
AU - Blom, Astrid
PY - 2018/4/1
Y1 - 2018/4/1
N2 - 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.
AB - 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.
KW - Ill-posedness
KW - Mixed sediment
KW - River morphodynamics
UR - http://www.scopus.com/inward/record.url?scp=85042462161&partnerID=8YFLogxK
UR - http://resolver.tudelft.nl/uuid:030c1056-2128-4bbf-a57b-0cf0fc3f6b30
U2 - 10.1016/j.advwatres.2018.02.011
DO - 10.1016/j.advwatres.2018.02.011
M3 - Article
AN - SCOPUS:85042462161
SN - 0309-1708
VL - 114
SP - 219
EP - 235
JO - Advances in Water Resources
JF - Advances in Water Resources
ER -