Numerical methods
Fluids & Geophysics

Numerical simulation of high density ratio gravity currents.
Application to the avalanches.

PhD Thesis, Institut National Polytechnique de Grenoble, September 2004

Flows of binary mixtures of incompressible, miscible fluids of very large density difference are considered. These flows are governed by the non-homogeneous Navier-Stokes equations, coupled with a convection-diffusion equation governing the evolution of the mixture composition. We present an algorithm that combines the method of characteristics, for the transport terms discretization, and the finite elements method with automatic mesh adaptation, and we prove that the solution obtained converges to the exact solution as the mesh and time steps go to zero. The robustness of this algorithm enables us to perform the first direct numerical simulations of lock-exchange flows with high density ratios, and to validate them by comparison with experiments. Dense cloud flows on slopes are also simulated, allowing to analyse the influence of the density ratio on the powder-snow avalanche flows.

Jury: M. Olivier PIRONNEAU, M. Jean-Paul VILA (reviewers), Mme Valérie PERRIER, M. Stéphane ZALESKI (examiners), M. Pierre SARAMITO, M. Emil HOPFINGER (PhD advisors).

the manuscript [in French, 3.5MB].