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A computational domain translation velocity is often used in LES simulationsto improve computational performance by allowing longer time-step intervals.Even though the equations of motion are Galilean invariant, LES results havebeen observed to depend on the translation velocity. It is found that LESresults of shallow convection depend on the domain translation velocity evenwhen a Galilean invariant formulation is used. This type of model error isnamed residual cross-grid flow error, to emphasize the expectation that itshould be negligible or zero. The residual gross-grid flow error is caused bybiases in finite difference dispersion errors. Schemes with low resolving power(typically low order of accuracy) produce larger dispersion errors that can beamplified by large-scale flow asymmetries, such as strong updrafts incumulus-cloud layers. Accordingly, the cross-grid flow error strongly dependson the order of accuracy of the numerical scheme progressively becomingnegligible as the order of accuracy is increased from second to sixth in thepresent simulations.

Residual cross-grid flow numerical error in large-eddy simulations of cumulus-topped boundary layers