Abstract
AbstractVariable resoltion methods can be divided in two groups, bridging and zonal methods. The bridging method is aimed to provide the best possible physical fidelity on any given numerical grid while varying seamlessly between Reynolds averaged Navier‐Stokes (RANS) model and Direct Numerical Simulations (DNS). Two of the most developed bridging methods are the partially integrated transport model (PITM) and partially averaged Navier‐Stokes (PANS) model. The PANS model was choosen here as the basic approach for the further theoretical extension but the conclusions derived in this work can be applied to the PITM model as well. It was shown in earlier studies that the implied cut‐off for the PANS method can be placed in any part of the spectrum including the dissipation range. This is done by varying the unresolved‐to‐total ratios of kinetic energy and dissipation. In the practice, the parameter which determines the unresolved‐to‐total kinetic energy ratio is defined by using the grid spacing and calculated integral length scale of turbulence. When the grid size is smaller, then more of the turbulent kinetic energy can be resolved. In the previous approach, the integral scale of turbulence is obtained by using resolved turbulence calculated as a difference between the instantaneous filtered velocity and the averaged velocity field. Such approach is impractical for cases with moving geometries or with transient boundaries. An alternative solution is to solve an additional equation for the resolved kinetic energy and then, the resolution parameter can be directly calculated as the equation for the unresolved kinetic energy is anyway solved. It must be only ensured that a modeled cut‐off length scale is larger than a numerical grid cell size. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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