An improved WENO method based on Gauss-kriging reconstruction with an optimized hyper-parameter

An adaptive finite-difference WENO method with Gauss-kriging reconstruction (we call it WENO-K) is proposed to reduce dissipation in smooth regions of flow while preserving high-resolution around discontinuities for hyperbolic system of conservation laws. The method adopts a kriging model with non-polynomial Gauss exponential function to obtain new reconstruction coefficients that contain a hyper-parameter. By adaptively optimizing the hyper-parameter and automatically identifying troubled cells using newly developed indicators, the accuracy in the smooth region is obviously improved. Compared with the classical WENO-JS method, the proposed WENO-K method provides more accurate reconstructions and sharper solution profiles near discontinuities. Furthermore, the WENO-K method is easy to implement in an existing classical WENO code with less than 13%-16% of additional computational cost. Numerical results demonstrate that the proposed method outperforms the WEND-JS method for a broad range of problems. This method is supposed to be applied to other variants of WENO scheme and offers the potential of improving their accuracy. (C) 2020 Elsevier Inc. All rights reserved.