Preconditioned boundary-implicit subiterative DDADI method for accuracy and efficiency enhancement in low-Mach number flows

For low-speed turbulent flows governed by compressible Navier-Stokes equations, the large disparity of phase velocities between hydrodynamic wave and acoustic wave leads to an ill-conditioned system where the numerical accuracy and efficiency are seriously affected. To tackle this issue, a preconditioned boundary implicit subiterative diagonally dominant alternating direction implicit (DDADI) method is proposed, where a series of accuracy and convergence enhancement techniques are combined, including the Weiss-Smith's preconditioning to reduce condition number, subiterative technique to eliminate approximation-factorization error in DDADI method, and boundary-implicit treatment to remove the accumulated error at multiblock interfaces. Several low-Mach number flows, consisting of inviscid, laminar, RANS steady flows and LES unsteady flows, are subsequently simulated to validate the good accuracy, strong robustness, and enhanced efficiency of the proposed method. Compared with unpreconditioning method, quantitative studies reveal that the residual convergence histories are significantly accelerated with preconditioning, as well as the accuracy being remarkably improved. Particularly, a low-Mach number flow past a generic-side view mirror is investigated to demonstrate the capability of present method in predicting the wavenumber-frequency spectra of the pressure fluctuations, where the acoustic and hydrodynamic modes of pressure fluctuations are both correctly presented. These results indicate that the proposed method would be a suitable selection for low-Mach turbulent and aeroacoustic problems.