Numerical Boundary Conditions for Specular Reflection in a Level-Sets-Based Wavefront Propagation Method

We study the simulation of specular reflection in a level set method implementation for wavefront propagation in high frequency acoustics using WENO spatial operators.To implement WENO efficiently andmaintain convergence rate,a rectangular grid is used over the physical space.When the physical domain does not conformto the rectangular grid,appropriate boundary conditions to represent reflection must be derived to apply at grid locations that are not coincident with the reflecting boundary.A related problem is the extraction of the normal vectors to the boundary,which are required to formulate the reflection condition.A separate level set method is applied to pre-compute the boundary normals which are then stored for use in the wavefront method.Two approaches to handling the reflection boundary condition are proposed and studied:one uses an approximation to the boundary location,and the other uses a local reflection principle.The second method is shown to produce superior results.

Simulation of Propagating Acoustic Wavefronts with Random Sound Speed

A method for simulating acoustic wavefronts propagating under random sound speed conditions is presented.The approach applies a level set method to solve the Eikonal equation of high frequency acoustics for surfaces of constant phase,instead of tracing rays.The Lagrangian nature often makes full-field ray solutions difficult to reconstruct.The level set method captures multiple-valued solutions on a fixed grid.It is straightforward to represent other sources of uncertainty in the input data using this model,which has an advantage over Monte Carlo approaches in that it yields an expression for the solution as a function of random variables.

An Application of the Level Set Method to Underwater Acoustic Propagation

An algorithm for computing wavefronts,based on the high frequency approximation to the wave equation,is presented.This technique applies the level set method to underwater acoustic wavefront propagation in the time domain.The level set method allows for computation of the acoustic phase function using established numerical techniques to solve a first order transport equation to a desired order of accuracy.Traditional methods for solving the eikonal equation directly on a fixed grid limit one to only the first arrivals,so these approaches are not useful when multi-path propagation is present.Applying the level set model to the problem allows for the time domain computation of the phase function on a fixed grid,without having to restrict to first arrival times.The implementation presented has no restrictions on range dependence or direction of travel,and offers improved efficiency over solving the full wave equation which under the high frequency assumption requires a large number of grid points to resolve the highly oscillatory solutions.Boundary conditions are discussed,and an approach is suggested for producing good results in the presence of boundary reflections.An efficientmethod to compute the amplitude from the level set method solutions is also presented.Comparisons to analytical solutions are presented where available,and numerical results are validated by comparing results with exact solutions where available,a full wave equation solver,and with wavefronts extracted from ray tracing software.