Finite-difference (FD) methods for the wave equation are flexible, robust and easy to implement. However, they in general suffer from numerical dispersion. FD methods based on accuracy give good dispersion at low frequencies, but waves tend to disperse for higher wavenumbers. Moreover, waves in higher dimensions also suffer from dispersion errors in all propagation angles. In this work, we give a unified methodology to derive dispersion reduction FD schemes for the two dimensional acoustic wave equation. This new methodology would generate schemes that give the theoretical minimum dispersion error in the uniform norm. Stability criteria are discussed for the general scheme. We also motivate the equivalence of popular dispersion reduction methodology and theoretical numerical reduction methodology.

波动方程的有限差分 (FD) 方法灵活、稳健且易于实现。然而，它们通常会受到数值分散的影响。基于精度的 FD 方法在低频下提供良好的色散，但波往往会在更高波数下发散。此外，更高维度的波在所有传播角度也会受到色散误差的影响。在这项工作中，我们给出了一种统一的方法来推导二维声波方程的色散减少 FD 方案。这种新方法将生成在统一范数中给出理论最小色散误差的方案。讨论了一般方案的稳定性标准。我们还鼓励流行的色散减少方法和理论数值减少方法的等效性。