A reduced order model including viscothermal losses

The Boundary Element Method (BEM) is a well-known numerical method for solving time harmonic acoustical problems. While the BEM has attractive features e.g. automatically satisfying the free field conditions, the frequency dependence of the Greens function makes is inconvenient for broadband simulations due to excessive computational costs. This problem becomes worse yet when viscous and thermal effects are included in the BE computations. Recently it has been suggested that a series expansion of the Greens function as well as its directional derivatives together with model order reduction techniques can relieve some of the computational demands. This paper applies similar ideas in the setting of the so-called boundary layer impedance boundary conditions used to approximate viscous and thermal effects. The final computational model can be used to efficiently perform broadband simulations including viscothermal losses of devices on the centimeter scale, thereby paving the path towards e.g. broadband shape optimization of small acoustical devices such as transducers, metamaterials and hearing aids.