Pressure fluctuations associated with turbulent boundary layer have been a prominent issue over the past few decades. In order to simulate pressure fluctuations beneath a turbulent boundary layer, a numerical investigation was performed in the current study. Four different turbulence models were employed to calculate the pressure and velocity fluctuations. A new approach of direct numerical simulation (DNS) was developed, as well. The proposed DNS scheme was hybrid of sixth-order weighted compact scheme (WCS) and modified weighted essentially non-oscillatory (WENO) scheme, which is called modified WENO-WCS scheme (MWWS) hereafter. A variety of benchmark problems were investigated to evaluate the accuracy of the proposed numerical scheme. Several empirical/semi-empirical mean square pressure models and single-point wall-pressure spectrum models were investigated to compare mean square wall pressure values. Reynolds-averaged Navier-Stokes based on Spalart-Allmaras (RANS-SA) and Delayed detached-eddy simulation based on Spalart-Allmaras (DDES-SA) turbulence models showed agreement with the Lowson, Lilley and Hodgson, and Goody models. Shear stress transport (RANS-SST) and DDES-SST models showed agreement with the Lowson, Farabee and Casarella, Lilley and Hodgson, and Goody models. The MWWS scheme was in agreement with Lowson and Goody models. Five single-point wall-pressure spectrum models were investigated and compared with numerical results. In low frequency region, results obtained by DDES-SA model and MWWS scheme were in agreement with the Goody model, while RANS-SA, RANS-SST, and DDES-SST turbulence models showed agreement with the Robertson model. In High frequency region, all investigated numerical methods were in agreement with the Goody and Efimtsov (1) models.