  This study proposes a level set-based topology optimization method for
designing acoustic structures with viscous and thermal boundary layers in
perspective. 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
approximately 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.
Moreover, the mechanisms that lead to the high absorption coefficient of the
optimized design are discussed.
