Numerical Wave Scattering Taking Account of Energy Dissipation and Media Stiffness as Modeled by the Telegraph Equation

Abstract

The telegraph equation is employed to model wave fields taking into account energy dissipation and media stiffness. The time-harmonic scattered waves generated by a line source incident upon cylindrical obstacles of arbitrary cross-section are studied. Solutions are found to depend strongly on the relative values of the frequency, damping, and stiffness coefficients. These coefficients are also found to have a significant effect on the far-field pattern. The analytical solution for a circular cylinder is reviewed. An approximate finite-difference solution is also obtained for the case of a two-dimensional scatterer with an arbitrary cross-section. Details are given for both soft and hard boundary conditions. The main feature of the numerical scheme is its computational efficiency based on the coupling between boundary conforming grids and a curvilinear coordinates version of the Dirichlet-to-Neumann non-reflecting boundary condition.