Implicit Large Eddy Simulation of weakly-compressible turbulent channel flow

• We present a comprehensive investigation of high-order Implicit Large Eddy Simulations in weakly compressible and turbulent channel flow.
• We show that low-Mach corrections significantly improve the accuracy of 2nd to 5th order ILES schemes.
• The WENO 9th-order scheme provides the best accuracy without using low Mach corrections.
• Detailed data for the accuracy vs associated computational cost for each ILES method are presented.

This paper concerns the accuracy of several high-resolution and high-order finite volume schemes in Implicit Large Eddy Simulation of weakly-compressible turbulent channel flow. The main objective is to investigate the properties of numerical schemes, originally designed for compressible flows, in low Mach compressible, near-wall turbulent flows. Variants of the Monotone Upstream-centred Scheme for Conservation Laws and Weighted Essentially Non-Oscillatory schemes for orders of accuracy ranging from second to ninth order, as well as with and without low Mach corrections, have been investigated. The performance of the schemes has been assessed against incompressible Direct Numerical Simulations. Detailed comparisons of the velocity profiles, turbulent shear stresses and higher-order turbulent statistics reveal that the low Mach correction can significantly reduce the numerical dissipation of the methods in low Mach boundary layer flows. The effects of the low Mach correction have more profound impact on second and third-order schemes, but they also improve the accuracy of fifth order schemes. The ninth-order Weighted Essentially Non-Oscillatory scheme is the least dissipative scheme and it is shown that the implementation of the low Mach correction in conjunction with this scheme has a significant anti-dissipative effect that adversely affects the accuracy. Finally, the computational cost required for obtaining the improved accuracy using increasingly higher order schemes is also discussed.