Two zonal wall models based on integral form of the boundary layer differential equations, albeit with algebraic complexity, have been implemented in an unstructured-grid cell-centered finite-volume LES solver. The first model is a novel implementation of the ODE equilibrium wall model, where the velocity profile is expressed in the integral form using the constant shear-stress layer assumption and the integral is evaluated using a spectral quadrature method, resulting in a local and algebraic (grid-free) formulation. The second model, which closely follows the integral wall model of Yang et al. (Phys. Fluids 27, 025112 (2015)), is based on the vertically-integrated thin-boundary-layer PDE along with a prescribed composite velocity profile in the wall-modeled region. Several numerical challenges unique to the implementation of these integral models in unstructured mesh environments, such as the exchange of wall quantities between wall faces and LES cells, and the computation of surface gradients, are identified and possible remedies are proposed. The performance of the wall models is assessed both in a priori and a posteriori settings against the traditional finite-volume based ODE equilibrium wall model, showing a comparable computational cost for the integral wall model, and superior performance for the spectral implementation over the finite-volume based approach. Load imbalance among the processors in parallel simulations seems to severely degrade the parallel efficiency of finite-volume based ODE wall model, whereas the spectral implementation is remarkably agnostic to these effects.

翻译：基于边界层微分方程积分形式（尽管具备代数复杂性）的两类分区壁面模型，已在非结构化网格单元中心有限体积LES求解器中实现。第一类模型是对ODE平衡壁面模型的新型实现，其采用恒定剪应力层假设将速度剖面表达为积分形式，并利用谱求积方法进行积分计算，从而得到局部代数化（无网格）公式。第二类模型紧密遵循Yang等人（Phys. Fluids 27, 025112 (2015)）提出的积分壁面模型，基于垂直积分薄边界层偏微分方程，并在壁面建模区域预设复合速度剖面。针对非结构化网格环境中实现这些积分模型时特有的数值挑战（例如壁面与LES单元之间的壁面量交换及表面梯度计算），本文识别了相关问题并提出了可能的解决方案。通过先验与后验两种评估模式，与传统有限体积ODE平衡壁面模型相比，积分壁面模型的计算成本相当，而谱实现方法相比有限体积方法展现出更优性能。并行模拟中的处理器负载不均衡现象可能严重降低基于有限体积的ODE壁面模型的并行效率，而谱实现方法对此类效应具有显著的不敏感性。