Predicting the arrival time of natural hazards such as tsunamis is of very high importance to the coastal community. One of the most effective techniques to predict tsunami propagation and arrival time is the utilization of numerical solutions. Numerical approaches of Nonlinear Shallow Water Equations (NLSWEs) and nonlinear Boussinesq-Type Equations (BTEs) are two of the most common numerical techniques for tsunami modeling and evaluation. BTEs use implicit schemes to achieve more accurate results compromising computational time, while NLSWEs are sometimes preferred due to their computational efficiency. Nonetheless, the term accounting for physical dispersion is not inherited in NLSWEs, calling for their consideration and evaluation. In the present study, the tsunami numerical model NAMI DANCE, which utilizes NLSWEs, is applied to previously reported problems in the literature using different grid sizes to investigate dispersion effects. Following certain conditions for grid size, time step and water depth, the simulation results show a fairly good agreement with the available models showing the capability of NAMI DANCE to capture small physical dispersion. It is confirmed that the current model is an acceptable alternative for BTEs when small dispersion effects are considered.