Contribution to the development of objective models for certain problems of fluid mechanics. Development of associated numerical methods

This document presents a synthesis of work carried out in the field of fluid mechanics, where a consistent description of fluid flows is proposed, in an incompressible or compressible, laminar or turbulent, monophasic or two-phase situation. Emphasis is placed on the respect of elementary properties such as objectivity, realizability for the turbulence models, and the guarantee of the positivity of the relevant variables more generally by the solutions of the PDE systems considered. For underlying hyperbolic systems, this regularly leads to the examination of solutions of one-dimensional Riemann problems. The synthesis thus comprises three distinct parts associated with the numerical simulation of laminar single-phase flows, the modeling and simulation of compressible or incompressible turbulent single-phase flows, and the modeling of two-phase flows comprising a compressible phase. Finite Volume techniques are systematically considered for the construction of unsteady algorithms