Temporal commutation errors in large-eddy simulation

The spatial filtering applied in large eddy simulations leads to additional closure problems if the filter width varies in space and time. While the spatial commutation error has been examined the temporal commutation error has not been studied despite its relevance for in-cylinder flow simulations [1]. Here some theoretical results for the temporal commutation error are presented. It is shown that a temporally varying domain leads to an additional constraint on the filter function. The results are illustrated for a simple scaler problem.