Journal of Computational Acoustics

A numerical algorithm has been developed to simulate linear wave propagation in media containing irregular inhomogeneities, especially irregular voids in fluids. The computational domain is extended to include the regions occupied by the inhomogeneities through replacing the boundaries with properly chosen sources. The solution corresponding to Dirichlet boundary conditions on the inhomogeneities is presented. This algorithm can be used to calculate linear wave propagation in a fluid medium with multiple bubbles.

Attenuation which is linear in frequency (as opposed to quadratic as for laminar viscosity) occurs in porous media wave propagation and biomedical applications. Straightforward use of Fourier transforms for frequency-linear attenuation violates causality. We give a causal time domain algorithm with numerical stability criteria and verify its accuracy. For acoustic wave propagation in ocean sediment, the algorithm results in a mild increase of phase speed with frequency as a result of the Kramers–Kronig relation. The algorithm gives results in good agreement with in situ data for sandy sediment.

The near sound field generated due to a vertically mounted circular cylinder piercing a free surface in shallow water, is studied computationally using the Large Eddy Simulation (LES) approach and the sound wave equation. The flow is simulated in both the air and water phases. The interface surface is allowed to move and is simulated using the Volume of Fluid technique. The pressure distribution over the cylinder is fed back into the sound wave equation to calculate the near field. The interface surface is modeled as a zero pressure surface in the acoustic calculation and the bottom is taken as having infinite impedence modeling the case of a rigid floor. Two of acoustic calculations methods are used. In the first method, the interface surface is assumed to be fixed and the wave equation is solved in the frequency domain in a post-processing stage. In the second method, the evolution of the interface surface is taken into account and the wave equation is simulated simultaneously with the LES. Both solutions are analyzed and compared to show that the interface surface acts as a strong damper to the low frequency sound by damping the vortex Von Karman rollers as well as causing the low frequency component to be nonradiative. The variation of the near sound field with the water depth and Froude number is investigated and the propagation and damping characteristics are analyzed.

A Chebyshev spectral element approximation of acoustic propagation problems based on linearized Euler equations is introduced, and the numerical approach is based on spectral elements in space with first-order Clayton–Engquist–Majda absorbing boundary conditions and implicit Newmark method in time. An initial perturbation problem has been solved to test the accuracy and stability of the numerical method. Then the sound propagation by source terms is also studied, including the radiation of a monopole and dipolar source in both stationary medium and uniform mean flow. The numerical simulation leads to good results in both accuracy and stability. Compared with the analytical solutions, the numerical results show the advantages in spectral accuracy even with relatively fewer grid points. Moreover, the implicit Newmark method in time marching also presents its superiority in stability. Finally, a problem of sound propagation in pipes is simulated as well.