An efficient adaptive high-order scheme based on the WENO processle

In this paper, we propose an efficient adaptive scheme based on the WENO (weighted essentially non oscillatory) process for the hyperbolic conservation laws. This scheme achieves fifth order accuracy as the fifth order WENO scheme does. Also, due to its adaptive mechanism, the scheme deals with problems which contain both discontinuities and complex smooth regions much better than traditional high order schemes. In addition, the proposed scheme saves computational costs by avoiding solving redundant nonlinear weights in certain places. Systematic analyses and numerical tests show that our adaptive scheme is of a high level of robustness and resolution. (C) 2016 Elsevier Ltd. All rights reserved.