发表机构
Mahindra University; Malaviya National Institute of Technology; Indian Institute of Technology, Delhi（马欣德拉大学; 马拉维娅国立理工学院; 印度德里理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对特殊相对论流体力学数值模拟中特征型WENO格式成本高的问题，提出三种混合WENO格式，通过受扰单元指示器区分区域以平衡精度与效率，H1-WENO在二维测试中效率提升30%-40%。
AI 中文摘要
特殊相对论流体力学（SRHD）方程用于建模天体物理现象中遇到的高速流体流动，如喷流、超新星爆炸和伽马射线暴。由于其高度非线性的双曲性质，解常常产生强间断，使得设计稳定且精确的数值格式具有挑战性。尽管加权本质无振荡（WENO）格式广泛用于此类问题，但分量型WENO重构可能在间断附近产生虚假振荡。另一方面，特征型WENO重构为守恒律系统提供精确的无振荡解，但它需要在每个单元中计算特征向量，导致计算成本高。在这项工作中，我们旨在开发混合格式，使其保持特征型WENO的无振荡特性，同时成本更低。我们提出三种混合格式，即H1-WENO、H2-WENO和H3-WENO格式，基于从WENO格式的光滑性指示器构造的新的 troubled-cell indicator（ troubled-cell indicator 可译为“受扰单元指示器”）。所提出的受扰单元指示器能有效区分光滑区域和间断区域，使混合格式在光滑区域采用低成本的重构，仅在间断附近使用特征型WENO重构。数值实验表明，所提出的格式保留了特征型WENO方法的精度和鲁棒性，同时显著降低了计算成本。特别是，在二维测试案例中，H1-WENO格式与标准WENO格式相比，计算效率提高了约30%至40%。
英文摘要
Special relativistic hydrodynamics (SRHD) equations arise in the modeling of high-speed fluid flows encountered in astrophysical phenomena such as jets, supernova explosions, and gamma-ray bursts. Owing to their highly nonlinear hyperbolic nature, solutions often develop strong discontinuities, making the design of stable and accurate numerical schemes challenging. Although Weighted Essentially Non-Oscillatory (WENO) schemes are widely used for such problems, component-wise WENO reconstruction may produce spurious oscillations near discontinuities. On the other hand, characteristic-wise WENO reconstruction provides accurate non-oscillatory solutions for systems of conservation laws, but it involves the computation of eigenvectors in each cell, which leads to high computational cost. In this work, we intend to develop hybrid schemes which maintain the non-oscillatory feature of characteristic-wise WENO while being less costly. We propose three hybrid schemes, namely the H1-WENO, H2-WENO, and H3-WENO schemes, based on a new troubled-cell indicator constructed from the smoothness indicators of the WENO scheme. The proposed troubled-cell indicator effectively distinguishes smooth and discontinuous regions, allowing the hybrid schemes to employ inexpensive reconstructions in smooth regions and the characteristic-wise WENO reconstruction only near discontinuities. Numerical experiments demonstrate that the proposed schemes retain the accuracy and robustness of characteristic-wise WENO methods while significantly reducing the computational cost. In particular, the H1-WENO scheme achieves an approximately 30--40% improvement in computational efficiency compared to the standard WENO scheme in 2D test cases.
