Abstract This paper is concerned with the development of a Cartesian grid method for predicting the acoustic field scattered by complex geometries immersed in an infinite fluid. The sound wave in the fluid is formulated by the linearized Euler equations (LEEs), which are computed on a fixed Cartesian grid by using a fourth-order dispersion-relation-preserving (DRP) scheme. The solid object naturally cuts the underlying Cartesian grid with its geometrical boundary, which is modeled by the Lagrangian method. A sharp-interface Cartesian grid model based on the ghost-cell immersed boundary method is established to impose the non-penetrating conditions on the complex boundary of the solid. The values of the acoustic variables at the ghost points are constructed by a linear extrapolation in conjunction with a constrained moving least-squares (CMLS) interpolation method. The interpolation method is capable of eliminating the numerical instability encountered in the conventional moving least-squares (MLS) formulation. The perfectly matched layers are adopted to absorb the out-going sound waves without any reflections from the computational boundary to the interior domain. The proposed method is verified by several benchmark problems in computational aeroacoustics, including the initial value problem of a pressure perturbation scattered by a rigid cylinder, and Gaussian distributed acoustic sources scattered by a single cylinder or two cylinders. Application of the proposed method to the problem of acoustic waves scattered by solids with complex geometries is also presented to demonstrate the effectiveness and robustness of the method.

中文翻译：

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一种用于复杂几何结构时域声散射的锐界面笛卡尔网格方法

摘要 本文涉及笛卡尔网格方法的发展，用于预测浸入无限流体中的复杂几何体所散射的声场。流体中的声波由线性化欧拉方程 (LEE) 公式化，该方程使用四阶色散关系保持 (DRP) 方案在固定笛卡尔网格上计算。实体对象以其几何边界自然切割底层笛卡尔网格，该几何边界通过拉格朗日方法建模。建立了基于鬼胞浸入边界法的锐界面笛卡尔网格模型，对固体的复杂边界施加非穿透条件。鬼点处的声学变量值是通过线性外推结合约束移动最小二乘 (CMLS) 插值方法构建的。插值方法能够消除传统移动最小二乘 (MLS) 公式中遇到的数值不稳定性。采用完美匹配的层来吸收传出的声波，而没有从计算边界到内部域的任何反射。所提出的方法通过计算气动声学中的几个基准问题得到了验证，包括刚性圆柱体散射的压力扰动的初始值问题，以及单个圆柱体或两个圆柱体散射的高斯分布声源问题。