Feasibility investigation of compressible direct numerical simulation with a preconditioning method at extremely low Mach numbers

Compressible direct numerical simulation (DNS) with a preconditioning method is conducted for the turbulent channel flow of Re τ=180 at an extremely low Mach number of 0.005. The turbulence statistics are in excellent agreement with incompressible DNS results, which indicates that the preconditioning method is able to accurately simulate the turbulence at an extremely low Mach number under the condition of sufficient resolution without any subgrid scale model or special treatment of numerical dissipation. In addition, the effects of the computational time step are investigated. It is shown that when the time step is shorter than 0.32 wall units, accurate results can be obtained and the total computational time is independent of the length of the time step. This study thus validates the feasibility of the compressible DNS with a preconditioning method for an extremely low Mach number and provides useful guidelines for simulating turbulence.