Abstract
The trend in high-performance computing toward heterogeneous architectures, such modern computers with GPUs, favors simpler algorithms with more parallelism over complex schemes. One example of algorithms with a high level of intrinsic parallelism is explicit numerical schemes based on compact stencils. These schemes are applicable to important problems in physics and engineering such as flood waves, transport in porous media, and gas dynamics. In this paper we consider the implementation of modern high-resolution schemes for hyperbolic conservation laws on state-of-the-art GPUs and evaluate the performance and scalability.