Turbulence

Even with the capabilities of todays supercomputers and algorithms, it is not possible to compute high-Reynolds (Re) number turbulent flows directly, by fully resolving all relevant turbulent eddy motions in space and time. Instead, at least part of the unsteady turbulent motion must be approximated, to make these calculations feasible. The grand challenge is to develop simulation models that although may not be explicitly incorporating all dynamic eddy scales of the flow will still give accurate and reliable results for at least the large energy-containing scales of motion. The current drive is toward LES in which the large energy-containing structures are resolved, whereas the smaller, presumably more isotropic and universal, structures are filtered out and, therefore, their effects need to be modeled. This gives LES a much higher generality than industrial-standard ReynoldsAveraged Navier Stokes approaches, which solve equations averaged over time, spatially homogeneous directions, or across an ensemble of equivalent flows, and for which the entire turbulent spectrum is effectively modeled. Different approaches are available for deriving the LES equations and the associated subgrid scale (SGS) models required to handle the effects of the unresolved flow physics. In general, we need to distinguish between conventional LES and implicit LES (ILES) based on using non-oscillatory high-resolution finite volume methods.

Flow visualization of the Taylor-Green vortex (TGV). The TGV has been used as fundamental prototype for vortex stretching and consequent production of small-scale eddies, to address the basic dynamics of transition to turbulence based on Direct Numerical Simulation (DNS) [1]

Our work is focusing on ILES, where the effects of the SGS physics on the resolved scales are incorporated through functional reconstruction of the convective fluxes using non-oscillatory (but not necessarily monotonic) high-resolution finite-volume algorithms. Major properties of the implicit SGS model in flux-limiting-based ILES are related to (i) the choice of high- and low-order schemeswhere the former is well behaved in smooth flow regions, and the latter is well behaved near sharp gradients; (ii) the choice of flux limiter which determines how these schemes should be blended locally, depending on prescribed characterization of the flow smoothness. More generally, the implicit SGS model in ILES depends on the critical balance of the dissipation and dispersion contributions to the numerical solution, which strongly depend on the design details of each high resolution non-oscillatory finite volume method. The aim of our research is twofold: (i) to understand how different high-resolution and high-order methods influence results in turbulent flow simulations; (ii) bearing in mind the computational uncertainties of (i) to use ILES in the investigation of turbulent flows ranging from canonical problems to flows around/inside complex geometries. Indicative examples from canconical problems are provided below, while application of ILES to more complex problems, e.g. compressible turbulent mixing, unsteady separated flows and applied aerodynamics can be found in other sections of this website.

Iso-surfaces of vorticity in the near wall region of a turbulent channel flow using ILES in conjunction with MUSCL 2nd order (left) and WENO 9th order (right) schemes. Grid resolution 1283; Reynolds (Re) number 6887, based on the channel half height and bulk velocity, and Mach number of 0.2. The objective of this study [2] was to scrutinize the dissipation properties of several different lower and higher order schemes with reference to direct numerical simulations (DNS); assess the effects of gird resolution on ILES of near wall turbulence; and investigate the effects of low-Mach corrections in the turbulent statistics.

References

  • D. Drikakis, C. Fureby, F. Grinstein, D. Youngs, Simulation of Transition and Turbulence-Decay in Taylor-Green Vortex, Journal of Turbulence, 8, 1, 1-12, 2007.
  • Kokkinakis, D. Drikakis, On the Accuracy of MUSCL and WENO Schemes in Implicit Large Eddy Simulation of Weakly-Compressible Turbulent Channel Flow, Journal of Computational Physics, under review, 2014.
  • Thornber, D. Drikakis, D.L. Youngs, R.J.R. Williams, Physics of the single-shocked and reshocked RichtmyerMeshkov instability, Journal of Turbulence, Vol. 13, 10, 1-17, 2012.
  • Z.A. Rana, B. Thornber, D. Drikakis, On the importance of generating accurate turbulent boundary condition for unsteady simulations, Journal of Turbulence, Vol. 12, 2011.
  • IB. Thornber, A. Mosedale, D. Drikakis, On the implicit large eddy simulations of homogeneous decaying turbulence, Journal of Computational Physics, 226, 1902-1929, 2007.