  We address a numerical instability that arises in the directionally split
computation of hydrodynamic flows when shock fronts are parallel to a grid
plane. Transverse oscillations in pressure, density and temperature are
produced that are exacerbated by thermal instability when cooling is present,
forming post--shock `stripes'. These are orthogonal to the classic post--shock
'ringing' fluctuations. The resulting post--shock `striping' substantially
modifies the flow. We discuss three different methods to resolve this problem.
These include (1) a method based on artificial viscosity; (2) grid--jittering
and (3) a new localized oscillation filter that acts on specific grid cells in
the shock front. These methods are tested using a radiative wall shock problem
with an embedded shear layer. The artificial viscosity method is unsatisfactory
since, while it does reduce post--shock ringing, it does not eliminate the
stripes and the excessive shock broadening renders the calculation of cooling
inaccurate, resulting in an incorrect shock location. Grid--jittering
effectively counteracts striping. However, elsewhere on the grid, the shear
layer is unphysically diffused and this is highlighted in an extreme case. The
oscillation filter method removes stripes and permits other high velocity
gradient regions of the flow to evolve in a physically acceptable manner. It
also has the advantage of only acting on a small fraction of the cells in a two
or three dimensional simulation and does not significantly impair performance.
