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.<>