Systematic study of accuracy of wall-modeled large eddy simulation using uncertainty quantification techniques

Abstract

The predictive accuracy of wall-modeled large eddy simulation is studied by systematic simulation campaigns of turbulent channel flow. The effect of wall model, grid resolution and anisotropy, numerical convective scheme and subgrid-scale modeling is investigated. All of these factors affect the resulting accuracy, and their action is to a large extent intertwined. The wall model is of the wall-stress type, and its sensitivity to location of velocity sampling, as well as law of the wall's parameters is assessed. For efficient exploration of the model parameter space (anisotropic grid resolution and wall model parameter values), generalized polynomial chaos expansions are used to construct metamodels for the responses which are taken to be measures of the predictive error in quantities of interest (QoIs). The QoIs include the mean wall shear stress and profiles of the mean velocity, the turbulent kinetic energy, and the Reynolds shear stress. DNS data is used as reference. Within the tested framework, a particular second-order accurate CFD code (OpenFOAM), the results provide ample support for grid and method parameters recommendations which are proposed in the present paper, and which provide good results for the QoIs. Notably, good results are obtained with a grid with isotropic (cubic) hexahedral cells, with 15 000 cells per δ 3 , where δ is the channel half-height (or thickness of the turbulent boundary layer). The importance of providing enough numerical dissipation to obtain accurate QoIs is demonstrated. The main channel flow case investigated is Re τ = 5200, but extension to a wide range of Re-numbers is considered. Use of other numerical methods and software would likely modify these recommendations, at least slightly, but the proposed framework is fully applicable to investigate this as well. 1 density, respectively. In contrast, the size of the energetic structures in the outer layer of the TBL scales with the TBL thickness δ, where δ δ ν . The ratio of δ ν /δ decreases with the Reynolds (Re-)number. This results in the number of grid cells required for LES approximately scaling as Re 1.85 for a TBL affected by a weak pressure gradient, see [12,13,58].A possible strategy to circumvent this restrictive computational cost is to only aim for resolving the structures in the outer layer of TBL, and approximate the uncaptured effects in the near-wall region by some type of modeling. The resulting approach is referred to as wall-modeled (WM)LES, for which the required number of grid cells increases linearly with the Re-number [12,13], and hence leads to a large reduction in the computational cost as compared to classical LES, which is from hereon referred to as wall-resolving (WR)LES.Different methodologies have been proposed for wall modeling, see the reviews [7,29,42,52] and the references therein. A particular class referred to as wall-stress modeling is considered in the present study. The near-wall treatment in this type of modeling consists of accurately predicting the local value of the filtered wall sh...

Effects of numerical dissipation on the predictive accuracy of wall-modelled large-eddy simulation

“…The magnitude and behavior of this error are very similar to that exhibited by . This confirms the observation made in a previous study [16] that in the case of attached boundary layers the accuracy of the wall model is chiefly determined by the accuracy of the velocity signal that it bases its predictions on.…”

“…In OpenFOAM, the scheme using 25% upwinding is referred to as LUST (linear upwind stabilized transport). WMLES comparing LUST and linear interpolation with no upwinding have been conducted in previous studies [16], [22], with more favorable results for first-order statistics achieved using LUST. Here, the cases of 15% and 5% upwinding are additionally considered to get a clearer picture of how upwinding affects the results.…”

“…and focus on evaluating or improving the performance of the wall model, see, for example, [8]- [15]. However, a recent study [16] has shown that the other parameters of the simulation affect the accuracy of WMLES at least as much as the wall modelling. In particular, the role of numerical dissipation in the simulation was highlighted, with more dissipative schemes and subgrid scale models, somewhat surprisingly, leading to more accurate results for certain flow quantities.…”

Predictive Accuracy of Wall-Modelled Large-Eddy Simulation on Unstructured Grids

“…Both of them are second-order accurate and unbounded, however the numerical diffusion introduced by the upwind scheme is enough to restrict the effect of any introduced non-physical oscillation. This treatment of the convective terms has been shown to provide good results in previous WMLES studies on hexahedral meshes [21,29]. Furthermore, it has proven to be stable enough for simulations on unstructured meshes presented in this work.…”

“…Instead, the equations are considered to be implicitly filtered by the discretization procedure. The WALE model [22] is selected for modelling the subgrid scales based on its favourable performance in WMLES on structured meshes [29,33].…”