RULES FOR THE USE OF THESES

Large-eddy simulation is rapidly becoming the preferred method for calculations involv-ing turbulent phenomena. However, ltering equations as performed in traditional LES procedures leads to signicant problems. In this work we present some key components in the construction of a novel LES solver for compressible turbulent ow, designed to overcome most of the problems faced by traditional LES procedures. We describe the construction of the large-scale algorithm, which employs fairly standard numerical techniques to solve the Navier{Stokes equations. We validate the algorithm for both transonic and supersonic ow scenarios. We further explicitly show that the solver is capable of capturing boundary layer eects. We present a detailed derivation of the chaotic map termed the \compressible poor man's Navier{Stokes (CPMNS) equation " starting from the Navier{Stokes equations them-selves via a Galerkin procedure, which we propose to use as the uctuating component in the SGS model. We provide computational results to show that the chaotic map can produce a wide range of temporal behaviors when the bifurcation parameters are varied over their ranges of stable behaviors. Investigations of the overall dynamics of the CPMNS equation demonstrates that its use increases the potential realism of the corresponding SGS model