刊物主题:Algorithms; Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theoretical, Mathematical and Computational Physics;
出版者:Springer US
ISSN:1573-7691
卷排序:70
文摘
We present adaptive finite difference ENO/WENO methods with infinitely smooth radial basis functions (RBFs). These methods slightly perturb the polynomial reconstruction coefficients with RBFs as the reconstruction basis and enhance accuracy in the smooth region by locally optimizing the shape parameters. Compared to the classical ENO/WENO methods, the RBF-ENO/WENO methods provide more accurate reconstructions and sharper solution profiles near the jump discontinuity. Furthermore the RBF-ENO/WENO methods are easy to implement in the existing classical ENO/WENO code. The numerical results in 1D and 2D presented in this paper show that the proposed finite difference RBF-ENO/WENO methods perform better than the classical ENO/WENO methods.