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Section: New Results
A few words on the results of the year
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Analysis of models with constraints: existence of solutions for a multidimensional model [1].
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Analysis of the convergence of a particle approximation for a traffic flow model with constraints [2].
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Numerical study of a traffic flow model with constraints [3]
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Existence of martingale solutions for the stochastic isentropic Euler model [4]
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New approach to accelerate convergence of Newton's methods applied to highly nonlinear and heterogeneous porous media flow problems [5], [6]
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We provide the numerical analysis of Discrete Duality Finite Volume (DDFV) schemes on general meshes for the (linear) Stokes problem with Neumann boundary conditions (on a fraction of the boundary). We prove well-posedness for a stabilized version of the scheme and we derive some error estimates. Finally, our theoretical results are illustrated with numerical simulations and stabilized and unstabilized schemes are compared. [26]
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A new domain decomposition algorithm to couple a non-isothermal compositional liquid gas Darcy flow and a free gas flow occurring at the interface between the nuclear waste repository and the ventilation galleries. [16], [22]
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A new two-phase Darcy flow model in fractured porous medium with fractures represented as interfaces of co-dimension one coupled to the surrounding matrix. The model accounts accurately for highly discontinuous capillary pressures, for gravity in the fracture width and both for fractures acting as drains or barriers. [7], [18]
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Use of the code ComPASS at BRGM to study the hydrothermal system of Lamentin Bay in Martinique during the PhD thesis of Yannis Labeau from University of Martinique [14], [21]
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New explicit energy-momentum conserving scheme for Hamiltonian systems [28].
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Through the PhD of J. Llobell, progress have been made to set up new schemes on staggered grids for solving the Euler system of gas dynamics (full Euler equations, MUSCL version on MAC grids, Low Mach regimes).