Flux Reconstruction Implementation of an Algebraic Wall Model for Large-Eddy Simulation

Shi, Jingchang; Yan, Hong; Wang, Z. J.

doi:10.2514/1.j058957

Cited by 11 publications

(5 citation statements)

References 29 publications

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“…

{\boldsymbol{v}}_{m-\frac{1}{2}}^{com\ast }=0.

As reported in the literature, 20 this treatment may cause instability due to an under‐resolved velocity profile.…”

Section: Wall Boundary Conditions For the Fr Methodsmentioning

confidence: 79%

“…As reported in the literature, 20 this treatment may cause instability due to an under-resolved velocity profile.…”

Section: No-slipmentioning

confidence: 74%

“…However, a grid employed in WMLES will be too coarse to resolve the profile near the wall. Therefore, the gradient of physical quantities near the wall computed on a WMLES grid must contain significant errors and may cause numerical instability, as reported in References 15,19,20. We focus on the polynomial approximation of the gradient (auxiliary variable)

\nabla \mathbf{w}\in {P}^K

, which is common to other DFEMs.…”

Section: Wall Boundary Conditions For the Fr Methodsmentioning

confidence: 99%

“…This employs a specified velocity gradient to compute the common velocity. 11 Using Equation (20), it is ensured that the velocity profile matches the velocity gradient modeled by the wall model.…”

Section: Wm Gradientmentioning

confidence: 99%

“…Because the data sets in each cell are compact and data communication over the cell interface is minimal, these methods are very suitable for massively parallel computations. The WMLES approach can also be applied to high‐order DFEMs, and several studies have been done in References 13–20. Previous studies have reported deteriorated prediction accuracy and stability due to higher‐order polynomial approximations 14,18,19 .…”

Section: Introductionmentioning

confidence: 99%

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On robust boundary treatments for wall‐modeled LES with high‐order discontinuous finite element methods

Fukushima,

Haga

2024

Numerical Methods in Fluids

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SummaryTo robustly and accurately simulate wall‐bounded turbulent flows at high Reynolds numbers, we propose suitable boundary treatments for wall‐modeled large‐eddy simulation (WMLES) coupled with a high‐order flux reconstruction (FR) method. First, we show the need to impose an auxiliary boundary condition on auxiliary variables (solution gradients) that are commonly introduced in high‐order discontinuous finite element methods (DFEMs). Auxiliary boundary conditions are introduced in WMLES, where the grid resolution is too coarse to resolve the inner layer of a turbulent boundary layer. Another boundary treatment to further enhance stability with under‐resolved grids, is the use of a modal filter only in the wall‐normal direction of wall‐adjacent cells to remove the oscillations. A grid convergence study of turbulent channel flow with a high Reynolds number () shows that the present WMLES framework accurately predicts velocity profiles, Reynolds shear stress, and skin friction coefficients at the grid resolutions recommended in the literature. It was confirmed that a small amount of filtering is sufficient to stabilize computation, with negligible influence on prediction accuracy. In addition, non‐equilibrium periodic hill flow with a curved wall, including flow separation, reattachment, and acceleration at a high Reynolds number (), is reported. Considering stability and the prediction accuracy, we recommend a loose auxiliary wall boundary conditions with a less steep velocity gradient for WMLES using high‐order DFEMs.

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“…

{\boldsymbol{v}}_{m-\frac{1}{2}}^{com\ast }=0.

As reported in the literature, 20 this treatment may cause instability due to an under‐resolved velocity profile.…”

Section: Wall Boundary Conditions For the Fr Methodsmentioning

confidence: 79%

“…As reported in the literature, 20 this treatment may cause instability due to an under-resolved velocity profile.…”

Section: No-slipmentioning

confidence: 74%

\nabla \mathbf{w}\in {P}^K

, which is common to other DFEMs.…”

Section: Wall Boundary Conditions For the Fr Methodsmentioning

confidence: 99%

Section: Wm Gradientmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On robust boundary treatments for wall‐modeled LES with high‐order discontinuous finite element methods

Fukushima,

Haga

2024

Numerical Methods in Fluids

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A novel wall model for large-eddy simulation of the flow around a circular cylinder

Wu,

Chen,

et al. 2024

Physics of Fluids

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The massive flow separation in the flow around a circular cylinder is challenging for the large-eddy simulation (LES) using the traditional equilibrium wall model (EQWM) for accurate prediction. To address this problem, a data-driven-non-equilibrium wall model (DNEQWM) was developed based on the result of the high-fidelity wall-resolved LES (WRLES) and the theoretical analysis. A hybrid modeling strategy was adopted in DNEQWM to deal with different flow regions. An empirical formula based on the analysis of the WRLES result was used to compute the wall shear stress in the attached region while the integration of the Navier–Stokes (N–S) equation was used in the separated region. Both EQWM and DNEQWM were applied to the LES of the flow around a circular cylinder at a classical Reynolds number of 3900 to evaluate the performance of the new model. It was found that DNEQWM was significantly superior to EQWM based on the analyses of the results of global flow quantities, surface pressure distributions, and flow details of mean and fluctuation velocities and the Reynolds stress in the wake. Flow visualizations indicated that DNEQWM can effectively reproduce the phenomenon of alternative periodic vortex shedding in the wake. The computational cost of DNEQWM was slightly lower than that of EQWM and significantly less than that of WRLES. This study presents a practical methodology for the wall model for the LES of the flow around the bluff body with smooth curved surfaces.

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Calibrating sub-grid scale models for high-order wall-modeled large eddy simulation

Duan,

Wang

2024

Adv. Aerodyn.

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High-order methods have demonstrated orders of magnitude reduction in computational cost for large eddy simulation (LES) over low-order methods in the past decade. Most such simulations are wall-resolved implicit LES (ILES) without an explicit sub-grid scale (SGS) model. The use of high-order ILES for severely under-resolved LES such as wall-modeled LES (WMLES) often runs into robustness and accuracy issues due to the low dissipation embedded in these methods. In the present study, we investigate the performance of several popular SGS models, the static Smagorinsky model, the wall-adapting local eddy-viscosity (WALE) model and the Vreman model, to improve the robustness and accuracy of under-resolved LES using high-order methods. The models are implemented in the high-order unstructured grid LES solver called hpMusic based on the discontinuous flux reconstruction method. The length scales in these SGS models are calibrated using the direct numerical simulation (DNS) database for the turbulent channel flow problem. The Vreman model has been found to produce the most accurate and consistent results with a proper choice of the length scale for WMLES.

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Flux Reconstruction Implementation of an Algebraic Wall Model for Large-Eddy Simulation

Cited by 11 publications

References 29 publications

On robust boundary treatments for wall‐modeled LES with high‐order discontinuous finite element methods

On robust boundary treatments for wall‐modeled LES with high‐order discontinuous finite element methods

A novel wall model for large-eddy simulation of the flow around a circular cylinder

Calibrating sub-grid scale models for high-order wall-modeled large eddy simulation

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