Abstract
In the present study we discuss several modelling issues of powder-snow avalanche flows. We take a two-fluid modelling paradigm. For the sake of simplicity, we will restrict our attention to barotropic equations. We begin the exposition by a compressible model with two velocities for each fluid. However, this model may become non-hyperbolic and thus, represents serious challenges for numerical methods. To overcome these issues, we derive a single velocity model as a result of a relaxation process. This model can be easily shown to be hyperbolic for any reasonable equation of state. Finally, an incompressible limit of this model is derived.
Keywords
- Mach Number
- Strouhal Number
- Snow Avalanche
- Momentum Conservation Equation
- Viscous Stress Tensor
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Ancey, C., Bain, V., Bardou, E., Borrel, G., Burnet, R., Jarry, F., Kolbl, O., Meunier, M.: Dynamique des avalanches. Presses polytechniques et universitaires romandes (Lausanne, Suisse) (2006)
Baer, M., Nunziato, J.: A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials. Int. J. Multiphase Flow 12(6), 861–889 (1986)
Bresch, D., Desjardins, B., Ghidaglia, J.M., Grenier, E.: On global weak solutions to a generic two-fluid model. To appear in Arch. Ration. Mech. Anal. (2009)
Dias, F., Dutykh, D., Ghidaglia, J.M.: A two-fluid model for violent aerated flows. Submitted to Comput. Fluids (2008)
Dutykh, D.: Mathematical modelling of tsunami waves. Ph.D. thesis, École Normale Supérieure de Cachan (2007)
Dutykh, D., Acary-Robert, C., Bresch, D.: Numerical simulation of powder-snow avalanche interaction with an obstacle. Submitted to Appl. Math. Model. (2009)
Ishii, M.: Thermo-Fluid Dynamic Theory of Two-Phase Flow. Eyrolles, Paris (1975)
Issler, D.: Experimental information on the dynamics of dry-snow avalanches. In: Hutter, K., Kirchner, N. (eds.) Dynamic Response of Granular and Porous Materials Under Large and Catastrophic Deformations, vol. 11. Springer, Berlin (2003)
Johannesson, T., Gauer, P., Issler, P., Lied, K.: The design of avalanche protection dams. Tech. rep., European Commission (2009)
Lied, K.: Satsie: Avalanche studies and model validation in Europe. Tech. rep., European Commission (2006)
Meyapin, Y., Dutykh, D., Gisclon, M.: Velocity and energy relaxation in two-phase flows. Submitted to Eur. J. Mech. B / Fluids (2009)
Murrone, A., Guillard, H.: A five equation reduced model for compressible two phase flow problems. J. Comput. Phys. 202, 664–698 (2005)
Naaim-Bouvet, F., Naaim, M., Bacher, M., Heiligenstein, L.: Physical modelling of the interaction between powder avalanches and defence structures. Nat. Hazards Earth Syst. Sci. 2, 193–202 (2002)
Rastello, M., Hopfinger, E.: Sediment-entraining suspension clouds: a model of powder-snow avalanches. J. Fluid. Mech. 509, 181–206 (2004)
Rovarch, J.M.: Solveurs tridimensionnels pour les écoulements diphasiques avec transferts d’énergie. Ph.D. thesis, Ecole Normale Supérieure de Cachan (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Meyapin, Y., Dutykh, D., Gisclon, M. (2011). Two-Fluid Barotropic Models for Powder-Snow Avalanche Flows. In: Krause, E., Shokin, Y., Resch, M., Kröner, D., Shokina, N. (eds) Computational Science and High Performance Computing IV. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 115. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17770-5_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-17770-5_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17769-9
Online ISBN: 978-3-642-17770-5
eBook Packages: EngineeringEngineering (R0)