Initial velocity excitations are straightforward in the DW paradigm,
but can be less intuitive in the FDTD domain. It is well known that
velocity in a displacement-wave DW simulation is determined by the
difference of the right- and left-going waves
[441]. Specifically, initial velocity waves
can
be computed from from initial displacement waves
by spatially
differentiating
to obtain traveling slope waves
, multiplying by minus the tension
to obtain force
waves, and finally dividing by the wave impedance
to
obtain velocity waves:
We can see from Eq.(E.11) that such asymmetry can be caused by unequal weighting of and . For example, the initialization
corresponds to an impulse velocity excitation at position . In this case, both interleaved grids are excited.