The two main approaches to numerical prediction of turbulent flows that are the RANS method and the
LES method have long been developed independently from each other and there is a need in practice to bridge
these apparently different approaches. Relying upon the spectral theory background, it has been possible to
develop continuous hybrid methods that allow seamless coupling between RANS and LES. The derivation
of the PITM method is based on the dynamic equation of the two-point fluctuating velocity correlations
with extension to nonhomogeneous turbulence. Indeed, the two-point velocity correlation equation embodies
a detailed description of the turbulence field. Then, using Fourier transform and performing averaging on
spherical shells on the dynamic equation, leads formally to the evolution equation of the one-dimensional
spectral velocity correlation tensor. Exiled in one-dimensional space, the turbulence quantities are represented
by functions of the scalar wave number rather than the wave vector. These spectral equations have also been
the basis for developing one-dimensional non-isotropic spectral models [1, 2]. A partial integration over a split
spectrum, with a given partitioning understood as spectral filtering, yields the partial integrated transport
modeling (PITM) method that can be used for practical simulations of turbulent flows [3, 4]. As a result, new transport equations for the subfilter scale stresses and dissipation-rate have been obtained. In this formulation, the model is governed by a dimensionless parameter which involves the cutoff wave number and the turbulence length-scale. Previous
simulations have shown that the PITM method is able to reproduce fairly well a large variety of internal
and external flows out of spectral equilibrium in the energetic sense and spectral anisotropy sense. Because
advanced closures can be used to model the subfilter range, then, large filter widths can be used without
prejudice and as a result the computing time can be fairly reduced. The present paper considers various
applications such as rotating flows encountered in turbomachinery [6], pulsed turbulent flows [3], flows with
wall mass injection [4], flows with separation and reattachment of the boundary layer [7, 8] a mixing of
two turbulent flows of different scales [9], airfoil flows [10], and a flow in a small axisymmetric contraction
[11], while allowing a drastic reduction of the computational resources in comparison with the one required
for highly resolved LES.

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