  Moving mesh methods provide an efficient way of solving partial differential
equations for which large, localised variations in the solution necessitate
locally dense spatial meshes. In one-dimension, meshes are typically specified
using the arclength mesh density function. This choice is well-justified for
piecewise polynomial interpolants, but it is only justified for spectral
methods when model solutions include localised steep gradients. In this paper,
one-dimensional mesh density functions are presented which are based on a
spatially localised measure of the bandwidth of the approximated model
solution. In considering bandwidth, these mesh density functions are
well-justified for spectral methods, but are not strictly tied to the error
properties of any particular spatial interpolant, and are hence widely
applicable. The bandwidth mesh density functions are demonstrated by applying
periodic spectral and finite-difference moving mesh methods to a number of
model problems in acoustics. These problems include a heterogeneous advection
equation, the viscous Burgers' equation, and the Korteweg-de Vries equation.
Simulation results demonstrate solution convergence rates that are up to an
order of magnitude faster using the bandwidth mesh density functions than
uniform meshes, and around three times faster than those using the arclength
mesh density function.
