This paper proposes a level set-based topology optimization method for designing acoustic structures with viscous and thermal boundary layers in perspective. It is known that acoustic waves propagating in a narrow channel are damped by viscous and thermal boundary layers. To estimate these viscothermal effects, we first introduce a sequential linearized Navier-Stokes model based on three weakly coupled Helmholtz equations for viscous, thermal, and acoustic pressure fields. Then, the optimization problem is formulated, where a sound-absorbing structure comprising air and an isothermal rigid medium is targeted, and its sound absorption coefficient is set as an objective function. The adjoint variable method and the concept of the topological derivative are used to obtain design sensitivity. A level set-based topology optimization method is used to solve the optimization problem. Two-dimensional numerical examples are provided to support the validity of the proposed method. In addition, the mechanisms that lead to the high absorption coefficient of the optimized design are discussed.

中文翻译：

---

使用顺序线性化 Navier-Stokes 模型考虑粘性和热边界层的声学结构拓扑优化

本文提出了一种基于水平集的拓扑优化方法，用于设计具有粘性和热边界层的声学结构。众所周知，在狭窄通道中传播的声波会被粘性边界层和热边界层衰减。为了估计这些粘热效应，我们首先引入了一个基于三个弱耦合亥姆霍兹方程的连续线性纳维-斯托克斯模型，用于粘性、热和声压场。然后，制定优化问题，其中以包含空气和等温刚性介质的吸声结构为目标，并将其吸声系数设置为目标函数。伴随变量法和拓扑导数的概念用于获得设计灵敏度。使用基于水平集的拓扑优化方法来解决优化问题。提供了二维数值例子来支持所提出方法的有效性。此外，还讨论了导致优化设计的高吸收系数的机制。