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 and lead too much numerical dissipation to resolve fine flow structures. 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 a L2-norm regularized incremental-stencil WENO scheme. In this method, a new L2-norm regularization is introduced into the WENO weighting strategy to modulate the weights of incremental-width stencils by taking account the L2-norm error term. A high-order non-dimensional discontinuity detector is then utilized as the regularization parameter for adaptive control. In addition, 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.

中文翻译：

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可压缩流的 L2 范数正则化增量模板 WENO 方案

对于具有宽带长度尺度和不连续性的可压缩流动的模拟，使用增量模板尺寸而不是均匀模板尺寸的 WENO 方案有望提高鲁棒性和减少数值耗散。然而，在平滑区域中，由于与较大模板相比，平滑度指标中缺少高阶导数，可能会将较大的权重分配给较小的模板，并且可能会降低顺序精度并导致过多的数值耗散来解决细流结构。为了解决这个缺点，基于 WENO-IS [Wang et al., IJMF 104 (2018): 20-31] 的模板选择，我们提出了 L2-norm 正则化增量模板 WENO 方案。在这种方法中，WENO 加权策略中引入了新的 L2 范数正则化，以通过考虑 L2 范数误差项来调节增量宽度模板的权重。然后将高阶无量纲不连续检测器用作自适应控制的正则化参数。此外，采用混合方法进一步提高性能和计算效率。许多基准案例表明，本方案实现了非常好的鲁棒性和精细结构解析能力。