Mathematical and physical constraints on large-eddy simulation of turbulence

Recent progress in the theoretical foundations of large-eddy simulation is reviewed. Most of the work reported is motivated by conceptual difficulties encountered in applying the large eddy simulation method to inhomogeneous complex geometry flows. Among the topics covered are the problem of the lack of commutation between filtering and derivative operators for inhomogeneous flows, the issues of enforcing symmetry and realizability conditions in subgrid modeling, and the problem of unacceptably high numerical errors in large eddy simulation implementations with finite difference methods.