Log-layer Mismatch Research Articles

Physics-informed machine-learning solution to log-layer mismatch in wall-modeled large-eddy simulation

This study proposes a physics-informed machine learning to enable using the erroneous flow data at near-wall grid points as the input to the wall model in a wall-modeled large-eddy simulation (LES). The proposed neural network predicts the amount of numerical error in the near-wall grid-point data and inputs the physically correct flow variables into the wall model by correcting the near-wall error. The input and output features of the neural networks are selected based on the physical relations of the turbulent boundary layer for robustness against various Reynolds and Mach number conditions. The proposed neural networks allow the wall model to accurately predict the wall shear stress from the erroneous near-wall information and yields accurate predictions of the turbulence statistics. Additionally, the proposed physics-informed machine-learning approach reproduces the asymmetry in the probability density functions of the predicted wall shear stress observed in direct numerical simulations, while the conventional wall model with input away from the wall does not. The results suggest that using the near-wall information for wall modeling may increase the fidelity of the wall-modeled LES. Published by the American Physical Society 2024

A Hybrid Large Eddy Simulation Algorithm Based on the Implicit Domain Decomposition

The resolution of small near-wall eddies encountered in high-Reynolds number flows using large eddy simulation (LES) requires very fine meshes that may be computationally prohibitive. As a result, the use of wall-modeled LES as an alternative is becoming more popular. In this paper, the near-wall domain decomposition (NDD) approach that was originally developed for Reynolds-averaged Navier–Stokes simulations (RANSs) is extended to the hybrid RANS/LES zonal decomposition. The algorithm is implemented in two stages. First, the solution is computed everywhere with LES on a coarse grid using a new non-local slip boundary condition for the instantaneous velocity at the wall. The solution is then recomputed in the near-wall region with RANS. The slip boundary conditions used in the first stage guarantee that the composite solution is smooth at the inner/outer region interface. Another advantage of the model is that the turbulent viscosity in the inner region is computed based on the corresponding RANS velocity. This shows improvement over those hybrid models that have only one velocity field in the whole domain obtained from LES. The model is realized in the open source code OpenFOAM with different approximations of turbulent viscosity and is applied to the planar channel flow at frictional Reynolds numbers of Reτ=950, 2000, and 4200. Mean streamwise velocity and Reynolds stress intensities are predicted reasonably well in comparison to the solutions obtained with unresolved LES and available DNS benchmarks. No additional forcing at the interface is required, while the log–layer mismatch is essentially reduced in all cases.

A foundational step towards understanding and improving the transition between URANS and LES in hybrid URANS-LES methodology

Appropriate transition between URANS and LES plays an integral role in the performance of hybrid URANS-LES techniques. However, dynamics of the transition region (also known as the Gray Area) have not yet been well understood, despite several efforts to mitigate negative impacts of inappropriate modeling of this region such as deviation from law-of-the-wall (also referred to as log-layer mismatch (LLM)) in turbulent attached boundary layers. The current paper centers on Scale Adaptive Simulation (SAS) hybrid URANS-LES methods and aims to address some shortcomings of the SAS methodology while providing new insights into the dynamics of the Gray Area. More specifically, necessary requirements, including the length scale, grid design and underlying RANS model to appropriately model essential dynamics of the Gray Area and, thus, mitigating the log-layer mismatch, are presented, which could be used for broader framework of hybrid URANS/LES and probably wall-modeled LES approaches.SAS methods traditionally have difficulty transitioning from URANS to LES without a sufficiently unstable base flow. Here we introduce an improved triggering mechanism based on departure-from-equilibrium dynamics formulated for the SAS method, primarily to enable the model to transition from URANS to scale resolving mode in attached/mildly separated flows, a well-known deficiency of the classical SAS formulations. The improved triggering mechanism considers deviations from equilibrium through a vortex stretching term in the dynamical equation for turbulent dissipation rate. The present study demonstrates that the length scale obtained for the gray area using straightforward blending of URANS and LES regions results in inaccurate transition dynamics. Therefore, we introduce a transport equation for the length scale of energy-containing eddies that allows an appropriate transition of length scale from URANS to LES mode. The modified framework uses the k−ɛ−ζ−f model as the underlying RANS model and is shown to trigger a transition from URANS to LES in stable attached stationary turbulent channel flow and mitigate the log-layer mismatch problem to a great extent. When applied to flows that feature boundary layer separation (flow over a periodic hill and flow over the wall-mounted hump), the current hybrid framework delivers results in agreement with existing experimental data and comparable to high fidelity LES calculations.

Artificial neural network-based wall-modeled large-eddy simulations of turbulent channel and separated boundary layer flows

Wall-models in a large-eddy simulation (LES) are essential to alleviate the large near-wall resolution requirements for high-Reynolds-number turbulent flow simulations. Among the existing wall-models for a LES, an equilibrium wall-stress model has the highest computational efficiency. Because this model has limitations, such as a lack of non-equilibrium effects and the assumption of a particular law of the wall in the mean velocity, we propose artificial neural network-based wall-stress models (AWMs). The input variables for the AWMs are extracted from the decomposition of the skin-friction coefficient proposed by Fukagata et al. [1], and the AWMs are shown to be able to predict the wall-shear stress in complex flows accurately. The performance of the AWMs is tested for two types of flows, a fully developed turbulent channel flow and a separated turbulent boundary layer flow. A direct comparison of the turbulence statistics with those obtained by previous wall-models (i.e., a log-law-based wall-stress model and a non-equilibrium wall-stress model) shows that better predictions are achieved using the AWMs for both flows, even with untrained Reynolds numbers. When using a coarse grid along the wall-normal direction in wall-modeled LESs (WMLESs) with the AWMs, an upward shift of the mean velocity profile (positive log-layer mismatch, LLM) compared to direct numerical simulation data is found, consistent with previous studies. However, this LLM problem can be overcome by imposing a filtered wall-normal velocity at the wall that is dynamically determined based on the continuity equation and the Taylor series expansion within wall-adjacent cells.

A DDES Model with Subgrid-scale Eddy Viscosity for Turbulent Flow

The original (delayed) detached-eddy simulation ((D)DES), a widely used and efficient hybrid turbulence method, is confronted with some flaws containing grid-induced separation (GIS), log-layer mismatch (LLM), and slow RANS-LES transition. A novel hybrid turbulence model, namely production-limited eddy simulation (PLES), depleting the production through introducing the subarid-scale eddy viscosity is proposed. The simulation data of the zero-pressure gradient boundary layer proves that a good performance in mitigating the GIS issue is obtained from the PLES model. The results of the channel flows reveal that the PLES model has eliminated the LLM of the velocity. A good conformity is given for the backward-facing step flow in the PLES simulation, which proves that the PLES model is validated for complex flow. More turbulent scales in the shear layer are captured by the PLES model, which testifies that the PLES model has a faster RANS/LES switch than the IDDES model. The PLES model has a good performance in predicting the cylinder flow with coarser grid resolution. Due to the new LES mode, the PLES model behaves better than the IDDES model in simulating the cylinder flow. Furthermore, the PLES model allows one to use different LES model in the LES portion for other complex flows.

Wall modeling for large-eddy simulation on non-body-conforming Cartesian grids

In this paper a novel methodology is proposed for wall-modeled large eddy simulation (WMLES) on non-body-conforming Cartesian grids. The proposed WMLES employs a partial-slip velocity boundary condition to reduce conservation errors at the wall. In addition, since the slip velocity reduces the shear stress in the near-wall region, a modeled turbulence shear stress is introduced to maintain the shear-stress balance in the near-wall region. The proposed WMLES robustly predicts turbulence statistics in turbulent boundary layers developed on an inclined flat plate without showing log-layer mismatch.

Wall-modeled lattice Boltzmann large-eddy simulation of neutral atmospheric boundary layers

The lattice Boltzmann method (LBM) sees a growing popularity in the field of atmospheric sciences and wind energy, largely due to its excellent computational performance. Still, LBM large-eddy simulation (LES) studies of canonical atmospheric boundary layer flows remain limited. One reason for this is the early stage of development of LBM-specific wall models. In this work, we discuss LBM–LES of isothermal pressure-driven rough-wall boundary layers using a cumulant collision model. To that end, we also present a novel wall modeling approach, referred to as inverse momentum exchange method (iMEM). The iMEM enforces a wall shear stress at the off-wall grid points by adjusting the slip velocity in bounce-back boundary schemes. In contrast to other methods, the approach does not rely on the eddy viscosity, nor does it require the reconstruction of distribution functions. Initially, we investigate different aspects of the modeling of the wall shear stress, i.e., an averaging of the input velocity as well as the wall-normal distance of its sampling location. Particularly, sampling locations above the first off-wall node are found to be an effective measure to reduce the occurring log-layer mismatch. Furthermore, we analyze the turbulence statistics at different grid resolutions. The results are compared to phenomenological scaling laws, experimental, and numerical references. The analysis demonstrates a satisfactory performance of the numerical model, specifically when compared to a well-established mixed pseudo-spectral finite difference (PSFD) solver. Generally, the study underlines the suitability of the LBM and particularly the cumulant LBM for computationally efficient LES of wall-modeled boundary layer flows.

Effect of Wall Boundary Conditions on a Wall-Modeled Large-Eddy Simulation in a Finite-Difference Framework

We studied the effect of wall boundary conditions on the statistics in a wall-modeled large-eddy simulation (WMLES) of turbulent channel flows. Three different forms of the boundary condition based on the mean stress-balance equations were used to supply the correct mean wall shear stress for a wide range of Reynolds numbers and grid resolutions applicable to WMLES. In addition to the widely used Neumann boundary condition at the wall, we considered a case with a no-slip condition at the wall in which the wall stress was imposed by adjusting the value of the eddy viscosity at the wall. The results showed that the type of boundary condition utilized had an impact on the statistics (e.g., mean velocity profile and turbulence intensities) in the vicinity of the wall, especially at the first off-wall grid point. Augmenting the eddy viscosity at the wall resulted in improved predictions of statistics in the near-wall region, which should allow the use of information from the first off-wall grid point for wall models without additional spatial or temporal filtering. This boundary condition is easy to implement and provides a simple solution to the well-known log-layer mismatch in WMLES.

Time-averaging and temporal-filtering in wall-modeled large eddy simulation

A turbulent channel flow at a Reynolds number of Reτ=2000 is solved based on the spatially filtered Navier–Stokes equations using large eddy simulation and an in-house code. A nonequilibrium wall model is implemented to predict the flow in the wall layer based on the Reynolds-averaged approach. To mitigate the log-layer mismatch, which is often encountered in wall modeling, two temporal schemes are introduced to average the wall layer solution and to filter the flow information input to the wall layer. It is found that the time periods used for the time-averaging and temporal-filtering schemes affect the performance of the wall model. The results show that shorter time periods enable the wall model to respond to the flow structures in the outer layer and correctly predict the friction velocity. However, the prediction of the friction velocity also depends on the location of the matching point. Locating the matching point further from the wall results in better performance due to the compatibility of the subgrid scale model with the grid resolution further from the wall. The temporal-filtering scheme is used to remove nonessential high-frequency wavelengths that can disturb the functionality of wall modeling. Various combinations of the time-averaging and temporal-filtering time periods are investigated for different locations of the matching point. Overall, it is concluded that using a shorter period for time-averaging and a temporal-filtering period comparable to the turbulent diffusion timescale leads to improved results.

Wall-modeled large-eddy simulations of spanwise rotating turbulent channels—Comparing a physics-based approach and a data-based approach

We develop wall modeling capabilities for large-eddy simulations (LESs) of channel flow subjected to spanwise rotation. The developed models are used for flows at various Reynolds numbers and rotation numbers, with different grid resolutions and in differently sized computational domains. We compare a physics-based approach and a data-based machine learning approach. When pursuing a data-based approach, we use the available direct numerical simulation data as our training data. We highlight the difference between LES wall modeling, where one writes all flow quantities in a coordinate defined by the wall-normal direction and the near-wall flow direction, and Reynolds-averaged Navier-Stokes modeling, where one writes flow quantities in tensor forms. Pursuing a physics-based approach, we account for system rotation by reformulating the eddy viscosity in the wall model. Employing the reformulated eddy viscosity, the wall model is able to predict the mean flow correctly. Pursuing a data-based approach, we train a fully connected feed-forward neural network (FNN). The FNN is informed about our knowledge (although limited) on the mean flow. We then use the trained FNNs as wall models in wall modeled LES (WMLES) and show that it predicts the mean flow correctly. While it is not the focus of this study, special attention is paid to the problem of log-layer mismatch, which is common in WMLES. Our study shows that log-layer mismatch, or rather, linear-layer mismatch in WMLES of spanwise rotating channels, is not present at high rotation numbers, even when the wall-model/LES matching location is at the first grid point.

Modification to Improved Delayed Detached-Eddy Simulation Regarding the Log-Layer Mismatch

The wall-modeled large-eddy simulation branch of the widely used improved delayed detached-eddy simulation (IDDES) method is supposed to resolve the problems of log-layer mismatch and underprediction of skin friction, as claimed by the authors of the IDDES (Shur, M. L., Spalart, P. R., Strelets, M. K., and Travin, A. K., "A Hybrid RANS-LES Model with Delayed DES and Wall-Modeled LES Capabilities," International Journal of Heat and Fluid Flow, Vol. 29, 2008, pp. 1638–1649). But, some researchers did meet these problems when using the IDDES. Aiming at finding out the reason and seeking a remedy, an analysis of the IDDES is carried out that focuses on the relation between the wall-parallel grid size and the length scale of the energetic turbulent structures at the Reynolds-averaged Navier–Stokes (RANS)/large-eddy simulation (LES) interface, and it reveals that the flaw of the IDDES arises from the fact that, in the IDDES approach, the energetic, large-scale, and stress-carrying turbulent structures in the vicinity of the RANS/LES interface are essentially impossible to well resolve by the LES mode. On the basis of the analysis, a modification to the IDDES is proposed by moving the RANS/LES interface further away from the wall so that, at the RANS/LES interface, the wall-parallel grid size is sufficient to resolve the turbulent structures. The modification is simple in form but has clear physical meaning. Through a series of sensitivity tests, it can be concluded that the modified IDDES does resolve the problems of log-layer mismatch and underprediction of skin friction, and it is applicable to low-, moderate-, and high-Reynolds-number flat plate boundary-layer flows without exception.

Algebraic non-equilibrium wall-stress modeling for large eddy simulation based on analytical integration of the thin boundary-layer equation

An algebraic nonequilibrium wall-stress model for large eddy simulation is discussed. The ordinary differential equation (ODE) derived from the thin-layer approximated momentum equation, including the temporal, convection, and pressure gradient terms, is considered to form the wall-stress model. Based on the concept of the analytical wall function (AWF) for Reynolds-averaged turbulence models, the profile of the subgrid scale (SGS) eddy viscosity inside the wall-adjacent cells is modeled as a two-segment piecewise linear variations. This simplification makes it possible to analytically integrate the ODE near the wall to algebraically give the wall shear stress as the wall boundary condition for the momentum equation. By applying such integration to the wall-normal velocity component, the methodology to avoid the log-layer mismatch is also presented. Coupled with the standard Smagorinsky model, the proposed SGS-AWF shows good performance in turbulent channel flows at Reτ = 1000–5000 irrespective of the grid resolutions. This SGS-AWF is also confirmed to be superior to the traditional equilibrium wall-stress model in a turbulent backward-facing step flow.

A time-average filtering technique to improve the efficiency of two-layer wall models for large eddy simulation in complex geometries

Two-Layer wall models have been recurrently studied since they represent a good physical model for Large Eddy Simulations with underresolved wall regions. Specifically, those based on the Reynolds Averaged Navier-Stokes equations are of special interest, since they can be applied to a wide range of conditions including non-equilibrium flows. Nonetheless, these models are affected by two recurrent problems, the “log-layer mismatch” and the resolved Reynolds stresses inflow, which until now, have been dealt with separated techniques. In this work, a time-filtering methodology is applied to tackle both issues at once with a single and low-computational-cost step, easily applicable to complex three-dimensional geometries. The time-filtering technique has already been applied to other types of wall models to mitigate the “log-layer mismatch.” Now, it is applied for the first time in the Two-Layer wall model context, showing its ability not only in avoiding the mismatch issue but also in blocking the resolved Reynolds stress inflow, dramatically improving the wall model performance and generality compared to other existing implementations. A methodology to determine the necessary temporal filter length is proposed and validated in equilibrium and non-equilibrium conditions. Additionally, the filter size influence on large-scale unsteady flow motions is assessed. Good results are obtained in steady and unsteady flow regimes by suppressing the LES highest frequencies while taking into account large-scale temporal effects.

The Role of Forcing and Eddy Viscosity Variation on the Log-Layer Mismatch Observed in Wall-Modeled Large-Eddy Simulations

We investigate the role of eddy viscosity variation and the effect of zonal enforcement of the mass flow rate on the log-layer mismatch problem observed in turbulent channel flows. An analysis of the mean momentum balance shows that it lacks a degree-of-freedom (DOF) when eddy viscosity is large, and the mean velocity conforms to an incorrect profile. Zonal enforcement of the target flow rate introduces an additional degree-of-freedom to the mean momentum balance, similar to an external stochastic forcing term, leading to a significant reduction in the log-layer mismatch. We simulate turbulent channel flows at friction Reynolds numbers of 2000 and 5200 on coarse meshes that do not resolve the viscous sublayer. The second-order turbulence statistics agree well with the direct numerical simulation benchmark data when results are normalized by the velocity scale extracted from the filtered velocity field. Zonal enforcement of the flow rate also led to significant improvements in skin friction coefficients.

A semi-locally scaled eddy viscosity formulation for LES wall models and flows at high speeds

We show that the mean wall-shear stresses in wall-modeled large-eddy simulations (WMLES) of high-speed flows can be off by up to $$\approx 100\%$$ with respect to a DNS benchmark when using the van-Driest-based damping function, i.e., the conventional damping function. Errors in the WMLES-predicted wall-shear stresses are often attributed to the so-called log-layer mismatch, which, albeit also an error in wall-shear stresses $$\tau _\mathrm{w}$$ , is an error of about $$15\%$$ . The larger error identified here cannot be removed using the previously developed remedies for the log-layer mismatch. This error may be removed by using the semi-local scaling, i.e., $$l_\nu =\mu /\sqrt{\rho \tau _\mathrm{w}}$$ , in the damping function, where $$\mu $$ and $$\rho $$ are the local mean dynamic viscosity and density, respectively.

Log-layer mismatch and modeling of the fluctuating wall stress in wall-modeled large-eddy simulations.

Log-layer mismatch refers to a chronic problem found in wall-modeled large-eddy simulation (WMLES) or detached-eddy simulation, where the modeled wall-shear stress deviates from the true one by approximately 15%. Many efforts have been made to resolve this mismatch. The often-usedfixes, which are generally ad hoc, include modifying subgridscale stress models, adding a stochastic forcing, and moving the LES-wall-model matching location away from the wall. An analysis motivated by the integral wall-model formalism suggests that log-layer mismatch is resolved by the built-in physics-based temporal filtering. In this work we investigate in detail the effects of local filtering on log-layer mismatch. We show that both local temporal filtering and local wall-parallel filtering resolve log-layer mismatch without moving the LES-wall-model matching location away from the wall. Additionally, we look into the momentum balance in the near-wall region to provide an alternative explanation of how LLM occurs, which does not necessarily rely on the numerical-error argument. While filtering resolves log-layer mismatch, the quality of the wall-shear stress fluctuations predicted by WMLES does not improve with our remedy. The wall-shear stress fluctuations are highly underpredicted due to the implied use of LES filtering. However, good agreement can be found when the WMLES data are compared to the direct numerical simulation data filtered at the corresponding WMLES resolutions.

A dynamic hybrid RANS/LES approach based on the local flow structure

By extracting the structural function from Vreman eddy-viscosity subgrid-scale model, a new turbulent length scale, which could quantify the degree of the instability of the local flow, is proposed. A hybrid RANS/LES method that combines both this kind of length scale and wall distance is obtained. The new model is capable of automatically determining the “transition” from RANS region to LES region according to the local flow state, instead of just taking the grid spacing into consideration. To investigate the WMLES (Wall-modeled LES) capability of this model, it is applied to fully-developed plane channel flows with two coarse grids whose grid numbers in wall parallel directions are respectively 37 × 37 and 49 × 49. Reτ ranges from 590 to 12,500. Most of the turbulent structures are resolved and sufficient resolved stresses are provided even near the wall. The prediction of mean velocity profiles is adequately accurate, and the phenomenon of “log layer mismatch” is removed. Flows pass a circular cylinder at subcritical Reynolds number is selected as an additional test case to explore the new model's performance subjected to separated flows. The present model has the potential of obtaining encouraging results with economical computation cost.

Effect of artificial length scales in large eddy simulation of a neutral atmospheric boundary layer flow: A simple solution to log-layer mismatch

A large eddy simulation (LES) methodology coupled with near-wall modeling has been implemented in the current study for high Re neutral atmospheric boundary layer flows using an exponentially accurate spectral element method in an open-source research code Nek5000. The effect of artificial length scales due to subgrid scale (SGS) and near wall modeling (NWM) on the scaling laws and structure of the inner and outer layer eddies is studied using varying SGS and NWM parameters in the spectral element framework. The study provides an understanding of the various length scales and dynamics of the eddies affected by the LES model and also the fundamental physics behind the inner and outer layer eddies which are responsible for the correct behavior of the mean statistics in accordance with the definition of equilibrium layers by Townsend. An economical and accurate LES model based on capturing the near wall coherent eddies has been designed, which is successful in eliminating the artificial length scale effects like the log-layer mismatch or the secondary peak generation in the streamwise variance.

A dynamic delayed detached-eddy simulation model for turbulent flows

Abstract The current study developed a new dynamic delayed detached-eddy simulation (dynamic DDES) model based on the k-ω SST model and the well-established dynamic k -equation subgrid-scale model. Instead of using a constant model coefficient C DES in traditional DES formulations, the present model employs two coefficients C k and C e , which are computed dynamically by taking into account the spatial and temporal variations of the flow field at the grid and test filter levels. A modification on shielding function f d is proposed, with a spatial uniformization operator imposed on the velocity gradient to obtain a smooth and monotonous hybrid interface. A damping function φ d is introduced based on the local grid resolution and flow condition to damp the Reynolds-averaged Navier–Stokes (RANS) region and achieve wall-modeled LES (WMLES) mode dynamically. The test of the model in developed channel flow shows the log-layer mismatch (LLM) problem is significantly improved with respect to the dynamic LES model and original DDES model. The use of the spatial uniformization operator and the damping function convincingly demonstrates the improvement in prediction of separated flows, with the model coefficients dynamically computed. The LES region is maximized at the limit of grid resolution and more turbulent vortical structures are resolved. The test in the ribbed channel flow shows the present model has considerably better performance in prediction of the mean and turbulence velocity in the strong shear layer and the recirculation bubble. In addition, the simulation of impinging jet shows the model exhibits rapid switching from the RANS to LES under the flow instabilities when the inflow does not include turbulence content.

On the dynamic computation of the model constant in delayed detached eddy simulation

The current work puts forth an implementation of a dynamic procedure to locally compute the value of the model constant CDES, as used in the eddy simulation branch of Delayed Detached Eddy Simulation (DDES). Former DDES formulations [P. R. Spalart et al., “A new version of detached-eddy simulation, resistant to ambiguous grid densities,” Theor. Comput. Fluid Dyn. 20, 181 (2006); M. S. Gritskevich et al., “Development of DDES and IDDES formulations for the k- ω shear stress transport model,” Flow, Turbul. Combust. 88, 431 (2012)] are not conducive to the implementation of a dynamic procedure due to uncertainty as to what form the eddy viscosity expression takes in the eddy simulation branch. However, a recent, alternate formulation [K. R. Reddy et al., “A DDES model with a Smagorinsky-type eddy viscosity formulation and log-layer mismatch correction,” Int. J. Heat Fluid Flow 50, 103 (2014)] casts the eddy viscosity in a form that is similar to the Smagorinsky, LES (Large Eddy Simulation) sub-grid viscosity. The resemblance to the Smagorinsky model allows the implementation of a dynamic procedure similar to that of Lilly [D. K. Lilly, “A proposed modification of the Germano subgrid-scale closure method,” Phys. Fluids A 4, 633 (1992)]. A limiting function is proposed which constrains the computed value of CDES, depending on the fineness of the grid and on the computed solution.