An algebraic variational multiscale‐multigrid‐multifractal method (AVM4) for large‐eddy simulation of turbulent variable–density flow at low Mach number

An algebraic variational multiscale‐multigrid‐multifractal method is proposed for large‐eddy simulation of turbulent variable‐density flow at low Mach number. In the multifractal subgrid‐scale modeling approach, the subgrid‐scale quantities are explicitly evaluated from a multifractal description of associated gradient fields. The multifractal subgrid‐scale modeling approach is embedded into a residual‐based form of the variational multiscale method. A particular feature of the proposed form of the multifractal subgrid‐scale modeling approach is scale separation by level‐transfer operators from plain aggregation algebraic multigrid methods to identify the required smaller resolved scales. In this study, we introduce a novel development of the multifractal subgrid‐scale modeling approach for application to turbulent variable–density flow at low Mach number. Based on the physical background, we derive a variable‐density extension of the multifractal subgrid‐scale modeling approach to recover the subgrid‐scale velocity and temperature field. The proposed method is validated via two numerical test cases. First, turbulent flow in a channel with a heated and a cooled wall is considered for two different temperature ratios. Second, turbulent flow over a backward‐facing step with heating is investigated. The results obtained with the algebraic variational multiscale‐multigrid‐multifractal method are compared with results obtained with the widely‐used dynamic Smagorinsky model and a residual‐based variational multiscale method. Particularly, the results obtained for turbulent flow in a channel with a heated and a cooled wall indicate the excellent prediction quality achievable by the proposed method for turbulent variable‐density flow at low Mach number. Copyright © 2014 John Wiley & Sons, Ltd.