The closure problem in large-eddy simulation from the viewpoint of information

A common misconception in large-eddy simulation (LES) modeling is that the closure problem of determining the subfilter-stress tensor arises from introducing the filter operator. Interestingly, this is not entirely accurate. Instead, an information-theoretic formalism shows that the closure problem is a consequence of the loss of information introduced by the filter, rather than the action of filtering itself. In general, reduced-order modeling, such as in LES, can be posed as a problem related to the conservation of information, where models aim to preserve the maximum amount of relevant information from the original system. In the case of LES, the actual closure problem emerges from the application of irreversible filters and/or the coarse discretization of the governing equations, which entail a truncation of the number of degrees of freedom in the system. In those situations, the LES grid resolution is unable to represent the small scales (i.e., subgrid scales), which in turn entails a loss of information. In this talk, we discuss the role of conservation of information as a fundamental aspect of LES modeling.