本研究旨在評估壁面模式大渦流模擬（Wall-Modeled Large Eddy Simulation, Wm-LES）於不同內流場的預測能力，並針對管道流與週期坡流場兩種典型流場進行模擬比較。在模擬中分別設定摩擦雷諾數〖 Re〗_τ=180 與 〖Re〗_τ=2000 的管道流，以及 Re=2800 與 Re=5600 的週期坡紊流，以探討 wall model 在不同雷諾數條件下之適用性。
數值方法採用壓縮流求解器搭配 Roe scheme 與預處理法以提升低速穩定性，並整合 Building Cube Method（BCM）與沉浸邊界法（Immersed Boundary Method, IBM）以處理複雜邊界幾何。壁面模型部分則基於管道紊流分佈與內插重建近壁速度，藉此在粗網格條件下保有速度梯度重建能力。
結果顯示，在〖 Re〗_τ=2000 管道流模擬中，Wm-LES 能顯著改善 LES 在高雷諾數下對速度與摩擦速度的預測誤差，誤差由 −12.1% 降至 −2.7%；紊流強度亦更接近 DNS 結果。對於週期坡流場，Wm-LES 在 Re=2800 時能合理預測分離與再附著位置。但在 Re=5600 條件下，因回流與非平衡效應增強，Wm-LES 存在再附著點提前、剪應力高估等問題，反映傳統 wall model 對逆壓梯與紊流再生的描述能力有限。整體而言，本研究驗證了 Wm-LES 在高雷諾數內流場模擬中的潛力與限制，並指出其未來於複雜分離流場中需進一步改良之方向。

The study investigates the predictive capability of wall model large eddy simulation (Wm-LES) in internal turbulent flows through comparative simulations of two canonical cases: channel flow and periodic hill flow. Simulations were performed at friction Reynolds numbers 〖Re〗_τ=180 and 〖Re〗_τ=2000 for channel flow, and bulk Reynolds numbers Re=2800 and Re=5600 for periodic hills, in order to evaluate the performance of Wm-LES across different flow regimes and Reynolds numbers.
The results show that for channel flow, Wm-LES significantly improves the accuracy of velocity profiles and wall shear stress compared to LES, particularly at high Reynolds numbers. The prediction error in friction velocity is reduced from −12.1% to −2.7%, and turbulence intensities in all three directions are closer to DNS references. In periodic hill flows, Wm-LES accurately captures flow separation and reattachment at Re=2800, with a reattachment location error under 0.2h. However, at Re=5600Re, the prediction degrades due to strong adverse pressure gradients and backflow, causing the reattachment point to shift by up to 0.4h and shear stress to be overestimated. These issues highlight the limitations of conventional wall models in handling complex, non-equilibrium near-wall conditions.
In summary, the study demonstrates the potential of Wm-LES in high-Reynolds-number simulations of attached flows, while identifying critical challenges in applying wall models to separated and recirculating flow fields. Future improvements may include developing backflow-aware or machine-learning-assisted wall models to enhance robustness in complex geometries.

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