Ground effects in time‐domain simulations of outdoor sound propagation.
Finite‐difference, time‐domain (FDTD) methods are precise and powerful tools to solve linearized Euler equations. Interaction between the acoustic waves with local wind or temperature gradients as well as a complex topography can be taken into account. Recently, a time‐domain boundary condition has been proposed [Cotte et al., AIAA J. 47, 2391–2403 (2009)] and has been implemented in a FDTD solver using methods developed in the computational aeroacoustics community [Bogey and Bailly, J. Comput. Phys. 194, 194–214 (2004)]. Propagation of an initial pulse over a distance of 500 m in a two‐dimensional geometry is considered in a frequency band up to 1200 Hz. Surface waves which propagate close to and parallel to impedance grounds are exhibited. To validate the obtained results, a comparison is made in the time‐domain with an analytical solution. Ground effects are discussed depending on the impedance of the ground. [This work was performed using HPC resources from GENCI‐IDRIS (Grant 2009‐022203).]
Padé approximation in time-domain boundary conditions of porous surfaces.
Formulation and implementation of time-domain boundary conditions (TDBCs) at the surface of a reactive porous material are made challenging by the slow decay, complexity, or noncausal nature of many commonly used models of porous materials. In this paper, approaches are described that improve computational efficiency and enforce causality. One approach involves approximating the known TDBC for the modified Zwikker-Kosten impedance model as a summation of decaying exponential functions. A second approach, which can be applied to any impedance model, involves replacing the characteristic admittance with its Padé approximation. Then, approximating fractional derivatives with decaying exponentials, a causal and recursive TDBC is formulated.
A vertical eigenfunction expansion for the propagation of sound in a downward-refracting atmosphere over a complex impedance plane.
The propagation of sound in a stratified downward-refracting atmosphere over a complex impedance plane is studied. The problem is solved by separating the wave equation into vertical and horizontal parts. The vertical part has non-self-adjoint boundary conditions, so that the well-known expansion in orthonormal eigenfunctions cannot be used. Instead, a less widely known eigenfunction expansion for non-self-adjoint ordinary differential operators is employed. As in the self-adjoint case, this expansion separates the acoustic field into a ducted part, expressed as a sum over modes which decrease exponentially with height, and an upwardly propagating part, expressed as an integral over modes which are asymptotically (with height) plane waves. The eigenvalues associated with the modes in this eigenfunction expansion are, in general, complex valued. A technique is introduced which expresses the non-self-adjoint problem as a perturbation of a self-adjoint one, allowing one to efficiently find the complex eigenvalues without having to resort to searches in the complex plane. Finally, an application is made to a model for the nighttime boundary layer.