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Habilitation à diriger des recherches

Une variation sur les propriétés magiques de modèles de Boltzmann pour l'écoulement microscopique et macroscopique

Abstract : This manuscript is devoted to an investigation of various aspects of modelization with the approach of Lattice Boltzmann Equation - hydrodynamic and anisotropic advection-diffusion equations, directional finite-difference recurrence equations (equivalents to LBE schemes) and the links between their solutions and infinite Chapman-Enskog expansion, consistent models for microscopic and macroscopic flow and their coupling in porous media, two phase immiscible fluids and free interface flow, water behaviour in variably saturated soil combining theoretical and numerical tools. Argument of symmetry with respect to underlying velocity set guides our analysis beyond the second order. We find that certain magic combinations of relaxation parameters, related to hydrodynamic and kinetic collision modes, take a control over the localisation of boundaries and interfaces, impact the stability and truncation errors of the model, and, more generally, determine the exact parametrization of the modelled equations by the governing non-dimensional physical numbers, at least in stationary regime. Two-relaxations-time model, with one relaxation parameter for all symmetric and another one for all anti-symmetric collision modes, play a distinctive role in our study.
Keywords : HDR
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Habilitation à diriger des recherches
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Irina Ginzburg. Une variation sur les propriétés magiques de modèles de Boltzmann pour l'écoulement microscopique et macroscopique. Sciences de l'environnement. Thèse d'Habilitation à diriger des recherches Spécialité Sciences pour l'ingénieur, Université Pierre et Marie Curie Paris, 2009. ⟨tel-02591565⟩

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