Adaptive Mesh Refinement for Finite Difference WENO Schemes

In this paper, a high order fiWENO) scheme is combined with adaptive mesh refinement (AMR) to solve problems that require multi-resolution in space and time. Because conservative finite difference schemes of third or higher order of accuracy can only be achieved on uniform rectangular or smooth curvilinear meshes, either conservation or high order accuracy is lost when the WENO schemes are applied to the AMR framework. Several implementations are considered and compared to see which is more important: accuracy or conservation. The numerical experiments show that the general conservative implementation of AMR for finite-volume method can be used for high order WENO schemes without loss of much of accuracy