Extended reacting boundary modeling of porous materials with thin coverings for time-domain room acoustic simulations

Abstract

Modeling of acoustic boundary conditions has a significant impact on the accuracy of room acoustic simulations, which play an important role in the design phase of indoor built environments in order to improve the acoustical comfort. In this work, a numerical framework based on the discontinuous Galerkin (DG) method is presented for modeling extended reacting boundaries of porous absorbers covered by thin materials. The domain decomposition methodology is applied by treating the porous material as a subdomain. Equivalent fluid models are used to depict the acoustic properties of porous materials, whose effective density and compressibility as irrational functions are approximated by multipole rational functions in the frequency domain. By employing the auxiliary differential equation approach to calculate the time convolution, the augmented time-domain governing equations of porous materials can be expressed in the same unified hyperbolic form as the linear acoustic equations, which further enables a consistent upwind numerical flux formulation throughout the whole domain. The numerical coupling across the interface between propagation media is handled by solving the underlying Riemann problem. Compared to existing approaches with the DG method for extended reacting boundaries modeling for room acoustics, the derived upwind numerical flux formulation does not involve the computation of auxiliary variables. The presented framework yield a well-posed linear hyperbolic system with admissible boundary conditions as guided by the “uniform Kreiss condition” (Kreiss, 1970). Acoustic properties of the covering materials are illustrated by considering a limp permeable membrane model. A local time-stepping approach is utilized to improve computational efficiency. Numerical validations against analytical solutions in 1D are performed to verify the desired high-order convergence rate. A 3D case study on modeling spherical wave fronts demonstrates the broadband accuracy of the formulation.