This work forms part of a larger research project to develop efficient
low-dissipative high-order numerical techniques for high-speed
turbulent flow simulation, including shock wave interactions with
turbulence. The requirements on a numerical method are stringent.For
the turbulence the method must be capable of resolving accurately a
wide range of length scales, whilst for shock waves the method must be
stable and not generate excessive local oscillations. Conventional
methods are either too dissipative, or incapable of shock capturing.
Higher-order ENO, WENO or hybrid schemes are too expensive for
practical computations. Previous work of Yee, Sandham & Djomehri
(1999) developed high-order shock-capturing schemes which minimize the
use of numerical dissipation away from shock
waves. The objective of the present study is to further minimize the
use of numerical dissipation for shock-free compressible turbulence
simulations.