In the paper, a method to calculate the time evolution turbulence wavefronts based on the covariance method is theoretically presented in detail. According to it, the time-evolution wavefronts disturbed by atmospheric turbulence were experimentally generated by our LC atmospheric turbulence simulator (ATS) based on liquid crystal on silicon (LCOS) with high pixel density, and measured with a wavefront sensor. The advantage of such a LC ATS over a conventional one is that it is flexible with considering the weather parameters of wind speed and C(n) (2), and is relatively easy to control.