Abstract
A previous paper by Cimarelli et al. [“General formalism for a reduced description and modelling of momentum and energy transfer in turbulence,” J. Fluid Mech. 866, 865–896 (2019)] has shown that every decomposition of turbulent stresses is naturally approximated by a general form of tensorial eddy viscosity based on velocity increments. The generality of the formalism is such that it can also be used to give a reduced description of subgrid scalar fluxes. In the same work, this peculiar property of turbulent stresses and fluxes has been dynamically exploited to produce tensorial eddy viscosity models based on the second-order inertial properties of the grid element. The basic idea is that the anisotropic structure of the computational element directly impacts, although implicitly, the large resolved and small unresolved scale decomposition. In the present work, this new class of turbulence models is extended to compressible turbulence. A posteriori analysis of flow solutions in a compressible turbulent channel shows very promising results. The quality of the modeling approach is further assessed by addressing complex flow geometries, where the use of unstructured grids is demanded as in real world problems. Also in this case, a posteriori analysis of flow solutions in a periodic hill turbulent flow shows very good behavior. Overall, the generality of the formalism is found to allow for an accurate description of subgrid quantities in compressible conditions and in complex flows, independent of the discretization technique. Hence, we believe that the present class of turbulence closures is very promising for the applications typical of industry and geophysics.
Highlights
The old idea of Boussinesq2 of representing turbulent stress and turbulent dissipation by means of an eddy viscosity has been developed during the years following many distinct directions
The basic idea is that the anisotropic structure of the computational element directly impacts, implicitly, the large resolved and small unresolved scale decomposition
Based on the formalism of the generalized central moments introduced by Germano,18 algebraic rules that relate resolved quantities to turbulent stresses at different levels defined by a filtering procedure can be derived
Summary
The old idea of Boussinesq of representing turbulent stress and turbulent dissipation by means of an eddy viscosity has been developed during the years following many distinct directions. The Smagorinsky model, based on the assumptions of isotropic smallscale turbulence in equilibrium with large scales, is the best known example of scalar eddy viscosity. Non-isotropic grids are usually used in simulations of nonhomogeneous flows with the aim to better represent large anisotropic turbulent structures. The second is to test the modeling approach in complex flows where the use of unstructured grids is demanded, exploiting all the potential of the proposed turbulence closure. For this second purpose, the turbulent flow over periodic hills is considered.
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