Dynamic Subgrid-Scale Modeling for Large-Eddy Simulations in Complex Topologies

The dynamic eddy-viscosity relationship is a suitable choice for modeling the subgrid-scales (SGS) in a large-eddy simulation (LES) of complex turbulent flows in irregular domains. This algebraic relationship is easy to implement and its dynamic coefficient will give negligible turbulent viscosity contributions in the flow regions that are irrotational or laminar. Its fine-scale turbulence predictions can be qualitatively reasonable if the local grid resolution maintains the SGS field predominantly within the equilibrium range of turbulent energy spectra. This performance is given herein by two curvilinear coordinate forms of the dynamic Smagorinsky model that are formally derived and a-priori tested using the resolved physics of the cylinder wake. The conservative form evaluates the dynamic coefficient in the computational (transformed) space whereas its non-conservative counterpart operates in the physical domain. Although both forms equally captured the real normal SGS stress reasonably well, the real shear stress and dissipation rates were severely under-predicted. Mixing the eddy-viscosity choice with a scale-similarity model can ease this latter deficiency.