LES of shock wave / turbulent boundary layer interaction

Chapter 1
Introduction
Design of new high-speed vehicles requires a detailed knowledge of
the flow behavior at supersonic and hypersonic speeds. Traditionally, the
experiment was the major source of such knowledge. Growing computer
power and development of reliable numerical techniques made it possible
to obtain more detailed data from numerical modeling. Currently
the flow field around an entire aircraft configuration can be modeled
numerically based on inviscid and viscous models (Agarwal, 1999). Utilizing
the Euler equations allows to capture the global flow structure,
but because viscosity is neglected it cannot predict separation related to
viscous-inviscid interaction (e.g. Volkov et al. (2002); Volkov & Loginov
(2000)). Obtaining reliable results in case of turbulent flow, which is
virtually every flow encountered in practical applications, is even more
complicated. In spite of more than a century of research on turbulent
motion, a closed theory still does not exist. Shock waves and their
interaction with turbulent boundary layers are accompany flight at supersonic
speeds. The shock wave / turbulent boundary layer interaction
(SWTBLI) can have very complicated appearance. It usually occurs in
inlets, near deflected control surfaces, near surfaces junctions, and has
a big influence on structural loads, sometimes causing aircraft damage.
This necessitates a reliable prediction tool with the ability to capture all
relevant physical phenomena.
Two basic ways of computing turbulence have traditionally been direct
numerical simulation (DNS) and Reynolds-averaged (RANS) modeling.
In the former, the full, time-dependent, Navier-Stokes equations are
solved numerically, essentially without approximations. The results are
expected to be equivalent to experimental ones. In the latter, only the
statistical mean flow is computed, and the effect of the turbulent fluctuations
is modeled according to a variety of physical approximations. It
was realized early that direct numerical simulations were too expensive
for most cases of industrial interest, while Reynolds-averaged modeling
was too dependent on the characteristics of particular flows for being
generally applicable. Large-eddy simulations (LES) were developed as
an intermediate approximation between these two approaches, the general
idea being that the large, non-universal, scales of the flow were to