Assessment of WENO schemes for numerical simulation of some hyperbolic equations using GPU

In this paper we study the implementation of WENO schemes on Graphic Processor Unit (GPU). The GPU implementation of the schemes are described for different test cases. The test cases are chosen from the linear and nonlinear and also one- and two-dimensional hyperbolic equations. Both the CPU and GPU versions of all the solvers are developed. The computational time of each test case using different schemes is obtained and the speedups are reported for different number of grid points. Also, two different GPUs are utilized and an occupancy analysis is performed for each of the GPUs. The numerical experiments show the speedups for the WENO schemes are more than that of the first-order upwind scheme and are very promising. Furthermore, the occupancy analysis indicates the occupancy is optimal for the presented simulations.