Finite-difference time-domain modeling of elastic wave propagation in the cylindrical coordinate system

A finite-difference time-domain numerical model for studying the propagation and scattering of transient elastic waves in two-dimensional cylindrical geometry with arbitrary azimuthal symmetry is presented. This 2-D cylindrical formulation is based on the first-order velocity-stress coupled partial differential equations. It uses a second-order accurate finite-difference scheme on a grid staggered both in space and time. The transducer source is modeled by `equivalent´ initial conditions. Waves reaching the edge of the grid are attenuated to reduce the numerical reflection from the boundary. This model accurately accounts for the boundary conditions along both solid-solid and the solid-liquid interfaces and provides correct averaging for grid points on a boundary between materials. Numerical results of scattering of a Gaussian pulse are presented in time sequences