(2008) concluded that the filter width must be decoupled from the grid size in the vicinity of an interface between a coarse and a fine mesh. Moreover, the presence of sharp changes in the filter width is directly associated with commutation errors ( Geurts and Holm, 2006). In cases in which adaptive meshes with local refinement are used, sudden variations of the grid size can occur that result in sharp gradients in the eddy viscosity they can cause aliasing errors. Even in simple wall-bounded flows, for instance, the two definitions of h in (3.2) result in very different behaviors of Δ ‾ near a solid wall where the grid is usually refined: If the algebraic mean is used, Δ ‾ decreases (as does the integral scale L ≃ κ y, where κ is the von Kàrmàn constant) if the geometric one is employed, on the other hand, Δ ‾ remains nearly constant, while L decreases. By relating the filter width to the grid size, one is likely to lose the relationship between the filter width and the turbulence physics. When complex flows are simulated, however, it may not be possible to know, a priori, where the integral scale decreases (and refine the mesh in these regions). Thus, some attempt is made to decrease the filter width where the local integral scale is smaller. In most calculations the grid is refined in regions of the flow where large gradients are expected. More rigorously, one would want the LES to approach the DNS limit if both the filter width and the grid size are reduced to zero. Furthermore, performing grid-convergence studies is not straightforward since many turbulent statistics depend on Δ ‾.
#Eddy viscosity ratio external flow how to
This appears to be poor practice because it becomes unclear how to distinguish modeling from numerical errors. As a consequence, as h becomes smaller, so does Δ ‾, and the LES approaches a DNS. This choice, however, carries a number of implications, some of them undesirable: 1.Īs the grid is refined, the filter-width also decreases. Relating the filter width to the mesh size has a simple rationale: The smallest eddy that can be resolved, in a numerical calculation, has size proportional to the grid thus, the unresolved eddies are those smaller than the grid (hence the term “subgrid scale stresses”).
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