  Direct numerical simulation (DNS), mostly used in fundamental turbulence
research, is limited to low turbulent intensities due the current and future
computer resources. Standard turbulence models, like RaNS (Reynolds averaged
Navier-Stokes) and LES (Large Eddy Simulation), are applied to flows in
engineering, but they miss small scale effects, which are frequently of
importance, see e.g. the whole area of reactive flows, flows with apparent
Prandtl or Schmidt number effects, or even wall bounded flows. A recent
alternative to these standard approaches is the one-dimensional turbulence
(ODT) model, which is limited to 1D sub-domains. In two papers we will provide
a generalized filter strategy, called XLES (extended LES), including a formal
theory (part I) and one special approach in the XLES family of models, called
ODTLES (in part II (see Glawe et al. (2015))). ODTLES uses an ODT sub-grid
model to describe all turbulent scales not represented by XLES, which leaves
the larger scales to be simulated in 3D. This allows a turbulence modeling
approach with a 3D resolution mainly independent of the turbulent intensity.
Thus ODTLES is able to compute highly turbulent flows in domains of moderate
complexity affordably and including the full range of turbulent and diffusive
scales. The convergence of XLES to DNS is shown and the unconventional XLES
advection approach is investigated in basic numerical tests. In part II, highly
turbulent channel and duct flow results are discussed and show the future
potential of XLES and ODTLES.
