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For the simulation of compressible flow with a broadband of length scales anddiscontinuities, the WENO schemes using incremental stencil sizes other thanuniform ones are promising for more robustness and less numerical dissipation.However, in smooth region, large weights may be assigned to smaller stencilsdue to the lack of high-order derivatives in the smoothness indicator comparedwith that of larger stencils, and may degrade the order accuracy and lead toomuch numerical dissipation to resolve fine flow structures. In order to copewith this drawback, based on the stencil selection of WENO-IS [Wang et al.,IJMF 104 (2018): 20-31], we propose a L2-norm regularized incremental-stencilWENO scheme. In this method, a new L2-norm regularization is introduced intothe WENO weighting strategy to modulate the weights of incremental-widthstencils by taking account the L2-norm error term. A high-order non-dimensionaldiscontinuity detector is then utilized as the regularization parameter foradaptive control. In addition, a hybrid method is adopted to further improvethe performance and the computational efficiency. A number of benchmark casessuggest that the present scheme achieves very good robustness andfine-structure resolving capabilities.

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