  Numerical solutions to hyperbolic partial differential equations, involving
wave propagations in one direction, are subject to several specific errors,
such as numerical dispersion, dissipation or aliasing. In multi-dimensions,
where the waves propagate in all directions, there is an additional specific
error resulting from the discretization of spatial derivatives along grid
lines. Specifically, waves or wave packets in multi-dimensions propagate at
different phase or group velocities, respectively, along different directions.
A commonly used term for the aforementioned multidimensional discretization
error is the numerical anisotropy or isotropy error. In this review, the
numerical anisotropy is briefly described in the context of the wave equation
in multi-dimensions. Then, several important studies that were focused on
optimizations of finite difference schemes with the objective of reducing the
numerical anisotropy are discussed.
