Time-Dependent Scattering By A Sound-Hard Sphere
Tomas Virgen, Arnold Kim, PhD
Time-dependent scattering in three dimensions is a difficult mathematical problem to solve analytically and numerically. This problem has applications in many different fields including satellite imaging, acoustics, and the physics of colloids. We specifically consider the acoustics problem for scattering off a moving sound-hard sphere. This sound-hard boundary condition corresponds to a no-slip condition in which the surrounding fluid has no velocity on the boundary of the sphere. We seek to develop a new method of solving this problem based on the method of fundamental solutions. For this method, we approximate the scattered field as a linear combination of exact solutions of the wave equation, each of which is the response by a discrete source. The coefficients of each term in the scattered field are then determined as to satisfy the sound-hard boundary condition. This method leads to an effective and efficient computational method of solving this problem.