The faster growth curves in the speed of graphics processing units (GPUs) relative to CPUs have spawned a new area of development in computational technology. There is much potential in utilizing GPUs for solving evolutionary partial differential equations and producing the attendant visualization. We are concerned with modeling tsunami waves, where computational time is of extreme essence in broadcasting warnings. We employed an NVIDIA board on a MacPro to test the efficacy of the GPU on the set of shallow-water equations, and compared the relative speeds between CPU and GPU for two types of spatial discretization based on second-order finite differences and radial basis functions (RBFs). We found that the GPU produced a speedup by a factor of 8 in favor of the finite difference method and a factor of 7 for the RBF scheme. We also studied the atmospheric dynamics problem of swirling flows over a spherical surface and found a speedup of 5.3 by the GPU. The time steps employed for the RBF method are larger than those used in finite differences, because of the fewer number of nodal points needed by RBF. Thus, RBF acting in concert with GPU would hold great promise for tsunami modeling because of the spectacular reduction in the computational time.