Tuned liquid dampers (TLDs) are considered economical and effective dynamic vibration absorbers. They are increasingly being used to mitigate the dynamic resonant response of tall buildings and it is often designed to reduce the structure's acceleration at a serviceability limit state. Slat screens can increase the inherent damping factor of TLDs. They have been used as a common flow damping device in TLDs because of the simplicity of using them and also the ability to control their effects on the performance of a TLD. Two slat screens with the same solidity ratio and different patterns could have different effects on the TLD's performance. Many former numerical researches used the potential and linear theory as a base to describe the fluid flow behavior inside the TLD. The applicability of the linearized flow models was for the condition of the low amplitude of excitations. Under large excitation events such as high return period wind storms or earthquakes, the assumptions of linear theory are no longer valid. Moreover, in the linearized model, screens were modeled as a hydraulic resistance point as a function of the screen solidity ratio without the ability to consider the effect of screen pattern. In the present study, a numerical algorithm has been developed which can handle both the small and large amplitude of excitations. In this algorithm, the fluid flow through the screen is fully resolved and it can take into account the effect of the screen pattern on the TLD's performance. The major focus of this paper is to use this developed algorithm and conduct a numerical investigation to study the effects of the slat screen pattern on the inherent damping and natural frequency of the TLD, as the design parameters of the TLD. In this numerical investigation a selected TLD outfitted by different slat screens and interacted with the structure is exposed by both harmonic and random external excitations. The numerical results have been validated against experimental work. The effect of slat screen pattern on the damping effect and natural frequency of a TLD has been presented. Also in this study, two new parameters termed as slat ratio (SR) and effective solidity ratio (S_{eff}) are presented to imply the physical significance of screen pattern.