An L2-norm regularized incremental-stencil WENO scheme for compressible flows

Abstract

For the simulation of compressible flow with a broadband of length scales and discontinuities, the WENO schemes using incremental stencil sizes other than uniform ones are promising for more robustness and less numerical dissipation. However, in smooth region, large weights may be assigned to smaller stencils due to the lack of high-order derivatives in the smoothness indicator compared with that of larger stencils, and may degrade the order accuracy especially in the region near critical points. In order to cope with this drawback, based on the stencil selection of WENO-IS [Wang et al., IJMF 104 (2018): 20–31], we propose an L2-norm regularized incremental-stencil WENO scheme in this paper. In order to avoid the above mentioned order degeneration, a new L2-norm regularization is introduced into the WENO weighting strategy by taking account the L2-norm error term. In addition, a high-order non-dimensional discontinuity detector is utilized as the regularization parameter for adaptive control. Then, a hybrid method is adopted to further improve the performance and the computational efficiency. A number of benchmark cases suggest that the present scheme achieves very good robustness and fine-structure resolving capabilities.