Simulation of Turbulent Flow Past Bluff Bodies on Coarse Meshes Using General Galerkin Methods: Drag Crisis and Turbulent Euler Solutions

In recent years adaptive stabilized finite element methods, here referred to as General Galerkin (G2) methods, have been developed as a general methodology for the computation of mean value output in turbulent flow. In earlier work, in the setting of bluff body flow, the use of no slip boundary conditions has been shown to accurately capture the separation from a laminar boundary layer, in a number of benchmark problems. In this paper we extend the G2 method to problems with turbulent boundary layers, by including a simple wall-model in the form of a friction boundary condition, to account for the skin friction of the unresolved turbulent boundary layer. In particular, we use G2 to simulate drag crisis for a circular cylinder, by adjusting the friction parameter to match experimental results. By letting the Reynolds number go to infinity and the skin friction go to zero, we get a G2 method for the Euler equations with slip boundary conditions, which we here refer to as an EG2 method. The only parameter in the EG2 method is the discretization parameter, and we present computational results indicating that EG2 may be used to model very high Reynolds numbers flow, such as geophysical flow.