Approximate acoustic boundary conditions in the time-domain using volume penalization

Abstract

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.