Numerical investigation of fully developed channel flow using shock-capturing schemes

Abstract

The ability to simulate wall-bounded channel flows with second- and third-order shock-capturing schemes is tested on both subsonic and supersonic flow regimes, respectively at Mach 0.5 and 1.5. Direct numerical simulations (DNSs) and large-eddy simulations (LESs) are performed at Reynolds number 3000. In both flow regimes, results are compared with well-documented DNS, LES or experimental data. At Ma 0=0.5, a simple second-order centred scheme provides results in excellent agreement with incompressible DNS databases, while the addition of artificial or subgrid-scale (SGS) dissipation decreases the resolution accuracy giving just satisfactory results. At Ma 0=1.5, the second-order space accuracy is just sufficient to well resolve small turbulence scales on the chosen grid: without any dissipation models, such accuracy provides results in good agreement with reference data, while the addition of dissipation models considerably reduces the turbulence level and the flow appears almost laminar. Moreover, the use of explicit dissipative SGS models reduces the results accuracy. In both flow regimes, the numerical dissipation due to the discretization of the convective terms is also interpreted in terms of SGS dissipation in an LES context, yielding a generalised dynamic coefficient, equivalent to the dynamic coefficient of the Germano et al. [Phys. Fluids A 3(7) (1991) 1760] SGS model. This new generalised coefficient is thus developed to compare the order of magnitude of the intrinsic numerical dissipation of a shock-capturing scheme with respect to the SGS dissipation.