Multifractal subgrid-scale modeling within a variational multiscale method for large-eddy simulation of turbulent flow

Multifractal subgrid-scale modeling within a variational multiscale method 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, which constitutes a new application of the variational multiscale concept. A focus of this study is on the application of the multifractal subgrid-scale modeling approach to wall-bounded turbulent flow. Therefore, a near-wall limit of the multifractal subgrid-scale modeling approach is derived in this work. The novel computational approach of multifractal subgrid-scale modeling within a variational multiscale formulation is applied to turbulent channel flow at various Reynolds numbers, turbulent flow over a backward-facing step and turbulent flow past a square-section cylinder, which are three of the most important and widely-used benchmark examples for wall-bounded turbulent flow. All results presented in this study confirm a very good performance of the proposed method. Compared to a dynamic Smagorinsky model and a residual-based variational multiscale method, improved results are obtained. Moreover, it is demonstrated that the subgrid-scale energy transfer incorporated by the proposed method very well approximates the expected energy transfer as obtained from appropriately filtered direct numerical simulation data. The computational cost is notably reduced compared to a dynamic Smagorinsky model and only marginally increased compared to a residual-based variational multiscale method.