A new weighting method for improving the WENO‐Z scheme |
| |
| Authors: | Shengping Liu Yiqing Shen Fangjun Zeng Ming Yu |
| |
| Affiliation: | 1. State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China;2. School of Engineering Science, University of Chinese Academy of Sciences, Beijing, China;3. Institute of Applied Physics and Computational Mathematics, Beijing, China |
| |
| Abstract: | The calculation of the weight of each substencil is very important for a weighted essentially nonoscillatory (WENO) scheme to obtain high‐order accuracy in smooth regions and keep the essentially nonoscillatory property near discontinuities. The weighting function introduced in the WENO‐Z scheme provides a straightforward method to analyze the accuracy order in smooth regions. In this paper, we construct a new sixth‐order global smoothness indicator (GSI‐6) and a function about GSI‐6 and the local smoothness indicators (ISk) to calculate the weights. The analysis and numerical results show that, with the new weights, the scheme satisfies the sufficient condition for the fifth‐order convergence in smooth regions even at critical points. Meanwhile, it can also maintain low dissipation for discontinuous solutions due to relative large weights assigned to discontinuous substencils. |
| |
| Keywords: | global smoothness indicator low numerical dissipation weighting function WENO‐Z scheme |
|
|
