Residual-based multiscale turbulence modeling: Finite volume simulations of bypass transition

Variational multiscale concepts are used to construct subgrid-scale models for Large-Eddy Simulation (LES) of turbulence. The basic idea of this framework is to introduce, a priori, a decomposition of the solution into coarse and fine scales. The coarse scales are identified with the numerical approximation, while the fine scales are identified with the subgrid scales and need to be modeled. A residual-based fine-scale approximation is proposed by extending to the nonlinear realm algebraic approximations of the local Green's function. These approximations, based on the Stabilized Methods theory, may be thought of as the modeling component of the proposed approach. This new modeling concept is very different from the classical LES modeling ideas, which are dominated by the addition of ad hoc eddy viscosities.; These newer variational multiscale ideas, and the older variants, have been implemented in a finite volume program that has enjoyed widespread use in turbulence simulations. The difficult problem of simulating the bypass transition of a boundary layer is examined from the point of view of the variational multiscale method and classical LES. The aim was to solve this problem as an LES and demonstrate the efficacy of the new residual-based modeling ideas in the process. Independent of the LES method, it was found that in order to accurately simulate bypass transition, the decay of input homogeneous, isotropic, free-stream turbulence must be the same for all meshes. A procedure was developed that enabled simulation of consistent energy decay with the range of meshes considered. The formulation is outlined and numerical results are presented and compared to a conventional LES approach, DNS results and experimental data.; The new method performs as well as the state-of-the-art LES models and offers a promising new path for turbulence research in LES. However, it obviously needs further testing on a wider variety of flows and implementation in a variety of numerical frameworks before drawing definitive conclusions. The experience gained indicates that the particular numerical discretization method has an enormous impact upon the results, and its influence is often underestimated by practitioners evaluating models.