Abstract
We are interested in the simulation of shallow dense avalanches in which the snow is considered as a compressible viscoplastic fluid. Such models can be derived by taking the shallow water asymptotics of a 3D Navier–Stokes–Bingham system with free surface. From the numerical analysis point of view, such equations imply the construction of new schemes which are able to compute accurately stationary states. We here present a well-balanced finite volume/augmented Lagrangian method which couples well-balanced finite volume scheme for the spatial discretization with the augmented Lagrangian method to treat the optimization problem stemming from the Bingham nature of the flow equations considered here, namely a system close to the shallow water equations but with an equation on the velocity which includes the yield limit (due to the Bingham stress tensor).
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Acknowledgments
D.B. thanks Institut de la Montagne (Université de Savoie) for financial support through the PPF: “Mathématiques et avalanches de neige, une rencontre possible?”. E.D.F.N. has been partially supported by the Spanish Government Research project MTM2006-01275 and the Région Rhône-Alpes (France). P.V. is partially supported by French ANR-08-JCJC-0104-01 research grant, as well as IMUS (Sevilla, Spain).
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Bresch, D., Fernandez-Nieto, E.D., Ionescu, I., Vigneaux, P. (2011). Augmented Lagrangian/Well-Balanced Finite Volume Method for Compressible Viscoplastic Flows. In: Kuzmin, A. (eds) Computational Fluid Dynamics 2010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17884-9_33
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DOI: https://doi.org/10.1007/978-3-642-17884-9_33
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