numerical dispersion
File:Numerical dispersion of a pulse signal in 1D FDTD.ogg scheme. The pulse distorts as it propagates in a vacuum media.]]
In computational mathematics, numerical dispersion is a difficulty with computer simulations of continua (such as fluids) wherein the simulated medium exhibits a higher dispersivity than the true medium. This phenomenon can be particularly egregious when the system should not be dispersive at all, for example a fluid acquiring some spurious dispersion in a numerical model.
It occurs whenever the dispersion relation for the finite difference approximation is nonlinear.[http://glossary.ametsoc.org/wiki/Numerical_dispersion numerical dispersion.] Glossary of the American Meteorological Society; page last modified on 26 January 2012, at 19:36.{{cite web|url=https://web.archive.org/web/20171115140759/www.mathematik.uni-dortmund.de/~kuzmin/cfdintro/lecture10.pdf |title=lecture10.dvi |date= |accessdate=2021-02-16}} For these reasons, it is often seen as a numerical error.
Numerical dispersion is often identified, linked and compared with numerical diffusion,[http://people.maths.ox.ac.uk/trefethen/5all.pdf CHAPTER 5: Dissipation, Dispersion, and Group Velocity] TREFETHEN another artifact of similar origin.
Explanation
In simulations, time and space are divided into discrete grids and the continuous differential equations of motion (such as the Navier–Stokes equation) are discretized into finite-difference equations;{{cite web|url=https://ccrma.stanford.edu/~bilbao/booktop/node100.html|title=Numerical Dispersion|website=ccrma.stanford.edu}} these discrete equations are in general unidentical to the original differential equations, so the simulated system behaves differently than the intended physical system. The amount and character of the difference depends on the system being simulated and the type of discretization that is used.