A three-dimensional mathematical model of local climate based on the artificial compressibility approach is considered. No outer iterations are necessary in order to solve the diagnostic equation for the pressure in complex terrain. Higher order approximation schemes based on the splitting up method are used for the advective operators of the problem. The turbulence parameterization scheme is based on the concept of computation of the mixing length. The dry atmospheric waves over a hill have been simulated. The results of the numerical experiments are in qualitative agreement with the theory available.