Multiscale Methods in Computational Mechanics

We present an apercu of our variational multiscale theory of LES turbulence. The theory is succinctly summarized in terms of a finite-dimensional coarse-scale equation governing the resolved scales that depend parametrically upon unresolved fine scales, which in turn are defined in terms of a functional of the coarse-scale residual “lifted” to the dual of the fine-scale space, and the coarse-scale velocity field itself. We illustrate the performance of a numerical implementation of the theory with calculations of a turbulent channel flow at a friction-velocity Reynolds number of 395 and comparisons with the DNS data.