A variational multiscale method with multifractal subgrid-scale modeling for large-eddy simulation of turbulent flow

Abstract

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 subgridscale 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. Two recent advancements to the proposed method are briefly addressed in this study. First, the application of the multifractal subgrid-scale modeling approach to wall-bounded turbulent flow is considered. For this purpose, a near-wall limit of the multifractal subgrid-scale modeling approach is derived. Second, the further development of multifractal subgrid-scale modeling within a variational multiscale method to turbulent variable-density flow at low Mach number is introduced. This extends the suggested subgrid-scale modeling approach to active scalar transport. The novel computational approach of multifractal subgrid-scale modeling within a variational multiscale formulation is then applied to turbulent incompressible flow over a backward-facing step and turbulent variable-density flow at low Mach number in a channel with a heated and a cooled wall. All results confirm a very good performance of the proposed method for both incompressible as well as variable-density flow. Notably improved results are obtained compared to a dynamic Smagorinsky model and a residual-based variational multiscale method.