Divergence-free turbulence inflow conditions for large-eddy simulations with incompressible flow solvers

• The divergence-free method generates synthetic turbulence correlated in time and space.
• The new method produces more reasonable pressure fluctuations compared to our previous method.
• In particular, the new method generates reasonable pressure fluctuation spectra.
• The new method requires no additional CPU time compared to our previous efficient method.
• The new method (including a slight modification of PISO) does not lead to solution divergence.

Synthetic turbulence for inflow conditions formulated on a 2-D plane generally produces unphysically large pressure fluctuations in direct numerical and large-eddy simulations. To reduce such artificial fluctuations a divergence-free method is developed with incompressible flow solvers. The procedure of the velocity–pressure solvers is slightly modified on a vertical plane near (rather than at) the inlet by inserting the synthetic turbulence on that plane during the procedure. Simple analytic and numerical error estimations are used to show that the impact of the modified solvers on solution accuracy is small. The final synthetic turbulence satisfies the divergence-free condition. No additional CPU time is required to achieve this condition. The method was tested via simulations of a plane channel flow with Reτ = 395. Reynolds stresses, wall skin friction and power spectra of velocity fluctuations are compared with those obtained from using periodic inlet–outlet boundary conditions. In particular, the variances and power spectra of pressure fluctuations are shown to be accurately predicted only when the divergence-free inlet condition is used.