| This dissertation develops and evaluates a high order method to compute wave scattering from moving boundaries. Specifically, we derive and evaluate a Discontinuous Galerkin Spectral elements method (DGSEM) with Arbitrary Lagrangian-Eulerian (ALE) mapping to compute conservation laws on moving meshes and numerical boundary conditions for Maxwell's equations, the linear Euler equations and the nonlinear Euler gas-dynamics equations to calculate the numerical flux on reflective moving boundaries. We use one of a family of explicit time integrators such as Adams-Bashforth or low storage explicit Runge-Kutta. The approximations preserve the discrete metric identities and the Discrete Geometric Conservation Law (DGCL) by construction. We present time-step refinement studies with moving meshes to validate the moving mesh approximations. The test problems include propagation of an electromagnetic gaussian plane wave, a cylindrical pressure wave propagating in a subsonic flow, and a vortex convecting in a uniform inviscid subsonic flow. Each problem is computed on a time-deforming mesh with three methods used to calculate the mesh velocities: From exact differentiation, from the integration of an acceleration equation, and from numerical differentiation of the mesh position. In addition, we also present four numerical examples using Maxwell's equations, one example using the linear Euler equations and one more example using nonlinear Euler equations to validate these approximations. These are: reflection of light from a constantly moving mirror, reflection of light from a constantly moving cylinder, reflection of light from a vibrating mirror, reflection of sound in linear acoustics and dipole sound generation by an oscillating cylinder in an inviscid flow. |
