Two-Dimensional Compact Third-Order Polynomial Reconstructions. Solving Nonconservative Hyperbolic Systems Using GPUs

We present a new kind of high-order reconstruction operator of polynomial type, which is used in combination with the scheme presented in Castro et al. (J. Sci. Comput. 39:67?C114, 2009) for solving nonconservative hyperbolic systems. The implementation of the scheme is carried out on Graphics Processing Units (GPUs), thus achieving a substantial improvement of the speedup with respect to normal CPUs. As an application, the two-dimensional shallow water equations with geometrical source term due to the bottom slope is considered.