Scholarlink

<p>In this paper, we propose a troubled-cell indicator in hybrid weighted essentially non-oscillatory (WENO) schemes by training an artificial neuron (AN), which is denoted as the AN indicator. The key idea of hybrid WENO schemes is to use discontinuity detectors to identify non-smooth regions, applying the costly WENO approximation in discontinuous regions and the cheaper linear approximation in smooth regions. The AN indicator has the advantages of being efficient, low dissipation, and high resolution. To analyze the performance of the AN indicator, we compare it with the multi-resolution (MR) indicator on one-dimensional (1D) uniform grids and the modified multi-resolution (MMR) indicator on two-dimensional (2D) unstructured triangular meshes for hyperbolic conservation laws. Numerical experiments show that, compared to the MR or MMR indicator, the AN indicator has a smaller percentage of reconstruction by the WENO approximation and more accurate numerical results. Moreover, these indicators significantly reduce computational costs.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The Artificial Neuron Indicator in Hybrid Weighted Essentially Non-oscillatory Schemes

  • 期刊论文

  • 发表日期：

    2026年1月8日

查看全文
  • Changna Lu,
  • Yuxing Miao,
  • Jingjin He,
  • Jin Wang

摘要

In this paper, we propose a troubled-cell indicator in hybrid weighted essentially non-oscillatory (WENO) schemes by training an artificial neuron (AN), which is denoted as the AN indicator. The key idea of hybrid WENO schemes is to use discontinuity detectors to identify non-smooth regions, applying the costly WENO approximation in discontinuous regions and the cheaper linear approximation in smooth regions. The AN indicator has the advantages of being efficient, low dissipation, and high resolution. To analyze the performance of the AN indicator, we compare it with the multi-resolution (MR) indicator on one-dimensional (1D) uniform grids and the modified multi-resolution (MMR) indicator on two-dimensional (2D) unstructured triangular meshes for hyperbolic conservation laws. Numerical experiments show that, compared to the MR or MMR indicator, the AN indicator has a smaller percentage of reconstruction by the WENO approximation and more accurate numerical results. Moreover, these indicators significantly reduce computational costs.