Performance of all-speed AUSM-family schemes for DNS of low Mach number turbulent channel flow

Abstract This article examines the performance of all-speed AUSM-family schemes in predicting low Mach number turbulent flow. A fully-developed turbulent channel flow at a friction velocity Reynolds number of 180 is solved as a benchmark problem. Direct numerical simulation is performed at Mach 0.3, 0.1 and 0.01, and the obtained results are compared with existing incompressible DNS results. The present DNS is performed by the AUSM+-up and SLAU schemes, and high-order spatial accuracy is achieved by using several variants of WENO interpolation methods. Numerical tests are performed at Mach 0.3, which is at the limit between compressible and incompressible flows. The results show that the all-speed AUSM-family schemes can compute turbulent channel flow, but great care must be taken to suppress the numerical dissipations inherent in WENO methods to solve turbulent flows accurately. Among the tested interpolation methods, WENO5-RL and WENO6-RL combined with Thornber’s low Mach number correction achieve excellent agreement with the incompressible pseudo-spectral DNS results, and they are recommended to be used in practical applications. DNSs are also performed at Mach 0.1 and 0.01, which are completely in incompressible flow. The obtained results show that the all-speed AUSM-family schemes can compute velocity field in turbulent channel flow accurately in the low Mach number regime. The results of RMS pressure fluctuations suggest that improvement is required for the prediction of small pressure fluctuations in the low Mach number regime.

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