Evaluating finite-difference operators applied to wave simulation
, by John T. Etgen
The continuous wave equation can be Fourier transformed over all spatial variables and over
time, and then solved for W as a function of spatial wavenumber. From the dispersion
relation, phase velocity or group velocity can be obtained. This procedure can also be
applied to discrete, finite-difference approximations to the acoustic or elastic wave
equation. Finite-difference solutions to the wave equation have different dispersion
relations than the continuous wave equation. The differences between the numerical and exact
phase velocities lead to errors commonly observed in finite-difference generated wave
fields. Understanding and counteracting these errors will lead to more accurate and
efficient techniques for solving wave equations on discrete grids.
STANFORD