Fachgebiet Numerische Fluiddynamik, Technische Universität Berlin, Müller-Breslau-Strasse 15, 10623 Berlin, Germany.
J Acoust Soc Am. 2023 Feb;153(2):1219. doi: 10.1121/10.0017347.
This paper presents an immersed boundary method for modeling complex impedance boundary conditions in wave-based finite-difference time-domain simulations. The fully parallelizable and physically motivated Brinkman method allows for the representation of complex geometries on simple Cartesian grids as porous material by introducing a friction term and an effective volume. The parameters are specified using blending functions, enabling impedance boundary conditions without the need for grid fitting or special boundary treatment. Representative acoustic configurations are analyzed to assess the method. In detail, acoustic materials on and in front of a rigid wall, a reacting surface as well as fully reflecting walls are examined. Comparison with analytical solutions shows satisfactory agreement of the resulting impedances in the range from 20 Hz up to 4 kHz. The method is derived for the (non-)linear Euler equations and the acoustic wave equation. An extensive stability analysis is carried out.
本文提出了一种基于浸入边界的方法，用于在基于波的有限差分时域模拟中建模复杂的阻抗边界条件。完全可并行化且符合物理原理的 Brinkman 方法通过引入摩擦项和有效体积，允许在简单的笛卡尔网格上表示复杂的几何形状作为多孔材料。参数使用混合函数指定，从而无需网格拟合或特殊边界处理即可实现阻抗边界条件。分析了代表性的声学配置以评估该方法。具体来说，研究了刚性墙上和前面的声学材料、反应表面以及完全反射壁。与解析解的比较表明，在 20 Hz 到 4 kHz 的范围内，得到的阻抗具有令人满意的一致性。该方法是针对（非）线性 Euler 方程和声波方程推导的。进行了广泛的稳定性分析。
