Atmospheric Sound Propagation Over Large-Scale Irregular Terrain

Abstract

A benchmark problem on atmospheric sound propagation over irregular terrain has been solved using a stable fourth-order accurate nite dierence approximation of a high-delity acoustic model. A comparison with the parabolic equation method and ray tracing methods is made. The results show that ray tracing methods can potentially be unreliable in the presence of irregular terrain.

High-fidelity numerical simulation of the dynamic beam equation

“…Remark The dispersion relation (3) shows that the wave speed scales as κ. Hence, the physics require k h 2 , to capture the high-frequency part of the solution.…”

“…Remark The dispersion relation (3) shows that the wave speed scales as κ. This means that we will have to take much smaller time-step (k) compared to the spatial grid-size (h), in order to resolve the fastest going waves (i.e., the high-frequency part of the solution).…”

High-Order Numerical Methods for 2D Parabolic Problems in Single and Composite Domains

“…In applications (Section 1), other geometries will likely be considered, some much more complicated than Figure 1. While our methods can handle more complicated geometry, this is (to the best of our knowledge) the first work looking to establish benchmarks -and compare numerical methods -for parabolic interface problems (3)(4)(5)(6)(7)(8)(9). As such, we think that the geometries in Figure 1 are a good "baseline"without all the added complexities that more complicated geometries might produce -from which further research, or more involved comparisons, might be done.…”

“…Let us now briefly introduce the DPM for the numerical approximation of parabolic interface models (3)(4)(5)(6)(7)(8)(9). First, we must introduce the point-sets that will be used throughout the DPM.…”

“…where v T H 2 v is the discrete energy for (49). In this paper, we use the spatial discretization operators developed in [75] to solve both the single (1,2) and composite domain problems (3)(4)(5)(6)(7)(8)(9). In [10], SBP-SAT-FD methods are discussed for the one-dimensional heat equation with constant coefficients, both in a single domain and a composite domain.…”