Comparison of numerical solvers for two-fluid turbulence processing

The aim of this thesis is to simulate a compressive turbulent multicomponent flow by different numerical methods. First of all, from a bibliographical analysis of turbulent models based on the statistical theory of splitting, a multicomponent model for turbulent flow is derived. The flow is supposed to be isentropic, like in the P-system. The evolution equation of the kinetic turbulent energy is established for the mixture. A generalization of the one-component turbulent equation is obtained. Following section is devoted to the exact resolution of the convective part of the system. The hyperbolicity is demonstrated and then, by an entropy criterion the unique solution is exhibited. If the initial states are not too far, the vacuum does not appear and the associated Riemann Problem admits a unique solution. In the last part, a generalization of this study to the multidimensional framework is done. Different tests of 2D multicomponent turbulent flows are introduced, and the results by a 1D comparison between the costly exact solver of the Godunov scheme and two linearized schemes are improved. Rusanov scheme and Vfroe-nc do not have the precision required in specific tests. The costly accuracy of Godunov scheme is justified. This work is continued with the diffusive part computation of the complete K-Epsilon model. (author)