Wall-modeled large eddy simulation (WMLES) is considered to be a powerful method in high Reynolds number wall-bounded fluid dynamics calculations. However, little research on aero-acoustic simulation by lattice Boltzmann method (LBM) combined with LES considering wall model has been found. Moreover, the discussion of the dominant geometric parameters of the wall model, which is dedicated to curved boundary modeling and based on a non-fitted Cartesian mesh, is rarely addressed. This paper proposes a WMLES algorithm based on a hierarchical Cartesian mesh and utilizing LBM, including the treatment of dominant geometric parameters. Firstly, based on the Green's formula, a strategy for obtaining detection point positions is developed using the mathematical formulas to solve the boundary free parameters, such as the normal direction of the curved surface and the distance from the lattice point to the solid-fluid boundary in the given direction. Secondly, a new wall model adapted to non-fitted Cartesian mesh is proposed to improve the precision of pressure fluctuation calculation. This model applies an interpolation bounce-back (IBB) scheme where slip velocity is estimated by an implicit wall function proposed by Spalart, and the eddy viscosity is reconstructed in the near-wall region. Finally, to enhance the accuracy of pressure fluctuation propagation, an appropriate transition zone treatment method of a multi-domain scheme with spatio-temporal second-order is applied and validated with a point source case. The aforementioned algorithms are implemented in a self-developed LBM code and validated through a three-element airfoil 30P30N benchmark, demonstrating their effectiveness and high accuracy in acoustic calculations.

壁面模型大涡模拟（WMLES）被认为是高雷诺数壁面边界流体动力学计算的强大方法。然而，考虑壁面模型的格子玻尔兹曼方法（LBM）结合大涡模拟（LES）进行气动声学模拟的研究还很少。此外，很少涉及专门用于弯曲边界建模并基于非拟合笛卡尔网格的墙模型的主要几何参数的讨论。本文提出了一种基于分层笛卡尔网格并利用 LBM 的 WMLES 算法，包括对主要几何参数的处理。首先，基于格林公式，利用数学公式求解曲面法线方向、格点到固液边界的距离等边界自由参数，制定了获取检测点位置的策略在给定的方向。其次，提出了一种适应非拟合笛卡尔网格的新型壁体模型，以提高压力脉动计算的精度。该模型采用插值反弹 (IBB) 方案，其中滑移速度由 Spalart 提出的隐式壁函数估计，并在近壁区域重建涡粘性。最后，为了提高压力脉动传播的精度，应用了时空二阶多域格式的适当过渡区处理方法，并通过点源案例进行了验证。上述算法以自主开发的LBM代码实现，并通过三元翼型30P30N基准测试进行验证，证明了其在声学计算中的有效性和高精度。