Numerical dispersion limits the application of numerical simulation methods for solving the acoustic wave equation in large-scale computation. The nearly analytic discrete method (NADM) and its improved version for suppressing numerical dispersion were developed recently. This new method is a refinement of two previous methods and further increases the ability of suppressing numerical dispersion for modeling acoustic wave propagation in 2D heterogeneous media, which uses acoustic wave displacement, particle velocity, and their gradients to restructure the acoustic wavefield via the truncated Taylor expansion and the high-order interpolation approximate method. For the method proposed, we investigate its implementation and compare it with the higher-order Lax-Wendroff correction (LWC) scheme, the original nearly analytic discrete method (NADM) and its im-proved version with regard to numerical dispersion, computational costs, and computer storage requirements. The numerical dispersion relations provided by the refined algorithm for 1D and 2D cases are analyzed, as well as the numerical results obtained by this method against the exact solution for the 2D acoustic case. Numerical results show that the refined method gives no visible numerical dispersion for very large spatial grid increments. It can simulate high-frequency wave propagation for a given grid interval and automatically suppress the numerical dispersion when the acoustic wave equation is discretized, when too few samples per wavelength are used, or when models have large velocity contrasts. Unlike the high-order LWC methods, our present method can save substantial computational costs and memory requirements because very large grid increments can be used. The refined method can be used for the simulation of large-scale wavefields.