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Description
The time-explicit discontinuous Galerkin finite element framework has been a powerful tool used for modelling of acoustic wave propagation in the time domain. Its applications stretch from room and underwater acoustics to medical and non-destructive inspection ultrasound and can be based on acoustic waves of small and finite amplitudes. The effective simulation of acoustic propagation in dissipative fluids requires accurate modelling of the sound dispersion and absorption. This can be challenging for the materials that obey a frequency power law attenuation, which is the case for many biological tissues.This work focuses on the development of a numerical approach based on the time-explicit discontinuous Galerkin framework for modelling of sound propagation in media that exhibit a power law attenuation. First, we derive the system of governing equations for small and finite amplitude propagation in media with relaxation starting from the constitutive equation and the conservation laws. Then, when the attenuation is given through a frequency power law, we apply the adaptive Antoulas-Anderson algorithm to get an "equivalent" relaxation process as a rational approximation of the dispersion relation within the given frequency range.