New results on turbulence generation and the effects for stabilized methods in turbulence simulation
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Simulation of turbulent flow is an outstanding challenge of computational mechanics, with respect to turbulence modeling, numerical methods and computational cost. A direct numerical simulation (DNS) computes a flow field on the finest turbulent scales, the Kolmogorov scales, whereas a large eddy sim- ulation (LES) seeks to compute a turbulent flow field on a truncated scale in the inertial subrange. The viability of LES relies in part on the concept of a turbulent energy cascade, a mechanism where energy is transferred in steps from a macroscopic scale down to the microscopic Kolmogorov scales, where LES corresponds to a truncation of such an energy transfer. In the context of stabilized and variational- multiscale finite element methods, this truncation is typically implemented through a residual-based subgrid/turbulence model. New results [1] identify a novel mechanism, which transfers energy directly from the macroscopic scale to the finest possible scale, without any step-wise process. Together with recent results on the stability of fundamental flow structures [3, 2], these findings have important consequences for stabilized and variational-multiscale methods [4] which we discuss in this work. REFERENCES [1] Hoffman J., Kronborg J., Turbulence generation supported by an inverse energy transfer through a zig-zag pattern, under review. [2] Hoffman J., Kronborg J., The triple decomposition of the velocity gradient tensor as a standardized real Schur form, Physics of Fluids, Vol.35(3), pp.031703, 2023. [3] Hoffman J., Energy stability analysis of turbulent incompressible flow based on the triple decomposition of the velocity gradient tensor, Physics of Fluids, Vol.33(8), pp.081707, 2021. [4] Hoffman J., Jansson J., Jansson N., Vilela De Abreu R., Towards a parameter-free method for high Reynolds number turbulent flow simulation based on adaptive finite element approximation, Computer Methods in Applied Mechanics and Engineering, Vol.288, pp.60-74, 2015.
