Adaptive modeling of turbulent flow with residual based turbulent kinetic energy dissipation

In this paper we first review our recent work on a new framework for adaptive turbulence simulation: we model turbulence by weak solutions to the Navier–Stokes equations that are wellposed with respect to mean value output in the form of functionals, and we use an adaptive finite element method to compute approximations with a posteriori error control based on the error in the functional output. We then derive a local energy estimate for a particular finite element method, which we connect to related work on dissipative weak Euler solutions with kinetic energy dissipation due to lack of local smoothness of the weak solutions. The ideas are illustrated by numerical results, where we observe a law of finite dissipation with respect to a decreasing mesh size.