Accurate modeling of pulse propagation and scattering is of great importance to the Navy. In a non-dispersive medium a fourth order in time and space 2-D Finite Difference Time Domain (FDTD) scheme representation of the linear wave equation can be used. However when the medium is dispersive one is required to take into account the frequency dependent attenuation and phase velocity. Using a theory first proposed by Blackstock, the linear wave equation has been modified by adding an additional term (the derivative of the convolution between the causal time domain propagation factor and the acoustic pressure) that takes into account the dispersive nature of the medium. This additional term transforms the calculation from one suitable to a workstation into one very much suited to a largescale computational platform, both in terms of computation and memory. With appropriate distribution of data, good scaling can be achieved up to thousands of processors. Due to the simple structure of the code, it is easily parallelized using three different techniques: pure MPI, pure OpenMP and a hybrid MPI/OpenMP. We use this real life application to evaluate the performance of the latest multi-cpu/multicore platforms available from the DoD HPCMP.