  A computational domain translation velocity is often used in LES simulations
to improve computational performance by allowing longer time-step intervals.
Even though the equations of motion are Galilean invariant, LES results have
been observed to depend on the translation velocity. It is found that LES
results of shallow convection depend on the domain translation velocity even
when a Galilean invariant formulation is used. This type of model error is
named residual cross-grid flow error, to emphasize the expectation that it
should be negligible or zero. The residual gross-grid flow error is caused by
biases in finite difference dispersion errors. Schemes with low resolving power
(typically low order of accuracy) produce larger dispersion errors that can be
amplified by large-scale flow asymmetries, such as strong updrafts in
cumulus-cloud layers. Accordingly, the cross-grid flow error strongly depends
on the order of accuracy of the numerical scheme progressively becoming
negligible as the order of accuracy is increased from second to sixth in the
present simulations.
