A Variational Multiscale Method with Multifractal Subgrid-scale Modeling for Large-eddy Simulation of Turbulent Flow

A variational multiscale method with multifractal subgrid-scale modeling is proposed for large-eddy simulation of turbulent flow. In the multifractal subgrid-scale modeling approach, the subgrid-scale velocity is evaluated from a multifractal description of the subgrid-scale vorticity, which is based on the multifractal scale similarity of gradient fields in turbulent flow. The multifractal subgrid-scale modeling approach is integrated into a variational multiscale formulation, demonstrating a new field of application of the variational multiscale concept. In addition, the application of the multifractal subgrid-scale modeling approach to wall-bounded turbulent flow is considered in this study. For this purpose, a nearwall limit of the multifractal subgrid-scale modeling approach is developed. The novel computational approach of multifractal subgrid-scale modeling within a variational multiscale formulation is then applied to turbulent flow over a backward-facing step. The results confirm a very good performance of the proposed method, and improved results are obtained compared to a dynamic Smagorinsky model and a residual-based variational multiscale method.