Abstract

In this work the scattering of an incident plane wave propagating along a plane perpendicular to the xy-plane is studied. The wave is scattered from an infinitely long cylindrical object of arbitrary cross-section. Due to the arbitrary geometry of the obstacle, a finite differences numerical method is employed to approximate the solution of the scattering problems. The wave equation is expressed in terms of generalized curvilinear coordinates. Boundary conforming grids are generated using elliptic grid generators. Then, a explicit marching in time scheme is implemented over these grids. It is found that as time grows the numerical solution converges to a wave with harmonic time dependence. The amplitude of these waves is analyzed and graphed over generalized grids for different geometries. An important physical measure of the energy scattered, the differential scattering cross section, is also obtained. In particular, the method is applied to a circular cylindrical obstacle. For this case, the analytical solution can also be obtained by traditional spectral techniques. The method is validated by comparing this exact solution with the numerical approximation obtained from the application of it.

Degree

College and Department

Physical and Mathematical Sciences; Mathematics

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