Study of precondition for simulating low-speed turbulence

Precondition for simulating low-speed turbulence is studied in this paper. Against the stiffness of the time-dependent scheme applied to low-speed turbulence, the precondition based on conservative variables is developed, which adopts an implicit iterative method for solving main control equations coupled with turbulence transport equations. In order to ensure the iterative solution stable, a reference Mach number, the dual-time stepping no-matrix scheme, and the method for processing implicitly the source terms of turbulence equations etc. have been developed reasonably, making the software platform unified for all-speed turbulence. Reference Mach number is defined in terms of global and local velocity by a single parameter, and the parameter can be used to control stability, numerical result accuracy, and switch of the precondition. The dual-time stepping LU-SGS method based on conservative variable precondition is developed, realizing no-matrix iterative solution for unsteady flow problems. Against the stiffness in solving the main control equations coupled with turbulence transport equations, the dissipation term of the turbulence equations is processed implicitly, which can enhance main diagonal dominance of the turbulence equations and make the iteration with greater stability. In simulating the turbulence in a nozzle and around a square cylinder or an airfoil, the precondition depicts correctly the structural character of the flowfield; and the computational results are in good agreement with those of theory and experiment etc., and its iterative convergence and numerical accuracy is excellent. It is shown that the precondition in this paper for low-speed turbulence is very effective.