Description
- Abstract:
- Computer models for underwater sound propagation often rely on ray tracing to obtain solutions to the high frequency wave equation. While adequate for large scale results in deep water environments, ray tracing has drawbacks that limit its reliability for simulations involving multiple boundary interactions and in studies concerning the effects of unmodeled physical processes. This work presents the development and application of the level set method to the high frequency wave equation with the intent of providing a framework for wavefront propagation in underwater acoustics as a valuable alternative to ray tracing. <br/> <br/> Level set methods are generic, computational models for solving dynamic interface problems. The model regularizes problems which exhibit behavior that is difficult to capture numerically in physical space by posing the problem in the higher-dimensional phase space. A relevant example is the behavior of self-intersecting wavefronts; in physical space, such solutions are multiple-valued. The level set method represents the interface implicitly as the zero level set of some function in the phase space, then propagates the surface according to a problem-dependent velocity field. Although the problem is posed in a higher dimensional space, the quantities of interest are local to the interface. Thus the computational burden may be reduced by solving the level set equations only in a neighborhood of the zero level set.<br/> <br/> The behavior of solutions at a reflecting boundary motivates the application of WENO methods, which are known to perform well on problems involving shocks. Since WENO methods are complicated to implement on irregular grids, two methods for applying reflection boundary conditions at an interface embedded within a Cartesian grid are proposed. In addition, this work develops a method for computing spreading loss via a semi-Lagrangian approach using the wavefronts provided by the level set solutions. A final topic is the application of a stochastic collocation method to study the effect of random perturbations in the wave speed on the wavefront propagation algorithm. Verification against a full wave equation solver and ray tracing software shows that the resulting method provides accurate wavefront information in the presence of multi-path propagation.<br/>
- Notes:
- Thesis (Ph.D. -- Brown University (2012)
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Citation
Martinelli, Sheri L.,
"A Level-Sets-Based Wavefront Propagation Method for Underwater Acoustics"
(2012).
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z0C24TQ1
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Applied Mathematics Theses and Dissertations
Theses and Dissertations for the Applied Mathematics department....