Investigation of all-speed schemes for turbulent simulations with low-speed features

Turbulence plays a key role in the aerospace design process. It is common that incompressible and compressible flows coexist in turbulent flows around aerospace vehicles. However, most upwind schemes in compressible solvers were designed to capture shock waves and have been proved to have difficulties in predicting low-speed flow regions. In order to overcome this defect, many all-speed schemes have been proposed. This paper investigates the properties of the all-speed schemes when applying to Reynolds averaged Navier-Stokes simulations with important low-speed features. First, the correctness of our code is validated. Then four test cases are adopted to evaluate the scheme performance, including a Mach 2.85 compression ramp, the NACA 4412 airfoil, a Mach 2.92 ramped cavity and a three-dimensional surface-mounted cube. Grid-converged results from the all-speed schemes show good agreement with the experimental data and remarkable improvement when compared to standard upwind schemes. Moreover, different from the traditional preconditioning methods, the all-speed schemes are simple to realize and free from the cut-off strategy or any problem-dependent parameter. Therefore, they are expected to be widely implemented into compressible solvers and applied to all-speed turbulent flow simulations.