In this paper, a fifth-order moment-based Hermite weighted essentially non-oscillatory scheme with unified stencils (termed as HWENO-U) is proposed for hyperbolic conservation laws. The main idea of the HWENO-U scheme is to modify the first-order moment by a HWENO limiter only in the time discretizations using the same information of spatial reconstructions, in which the limiter not only overcomes spurious oscillations well, but also ensures the stability of the fully-discrete scheme. For the HWENO reconstructions, a new scale-invariant nonlinear weight is designed by incorporating only the integral average values of the solution, which keeps all properties of the original one while is more robust for simulating challenging problems with sharp scale variations. Compared with previous HWENO schemes, the advantages of the HWENO-U scheme are: (1) a simpler implemented process involving only a single HWENO reconstruction applied throughout the entire procedures without any modifications for the governing equations; (2) increased efficiency by utilizing the same candidate stencils, reconstructed polynomials, and linear and nonlinear weights in both the HWENO limiter and spatial reconstructions; (3) reduced problem-specific dependencies and improved rationality, as the nonlinear weights are identical for the function $u$ and its non-zero multiple $\zeta u$. Besides, the proposed scheme retains the advantages of previous HWENO schemes, including compact reconstructed stencils and the utilization of artificial linear weights. Extensive benchmarks are carried out to validate the accuracy, efficiency, resolution, and robustness of the proposed scheme.

翻译：本文针对双曲守恒律提出了一种基于矩的五阶Hermite加权本质无振荡格式（简称HWENO-U）。HWENO-U格式的核心思想是：仅在时间离散中利用空间重构的相同信息，通过HWENO限制器修正一阶矩。该限制器不仅能有效抑制虚假振荡，还能保证全离散格式的稳定性。在HWENO重构中，我们设计了一种新的尺度不变非线性权重，该权重仅依赖于解的积分平均值，保留了原始权重的所有性质，在模拟具有剧烈尺度变化的挑战性问题时更加稳健。与现有HWENO格式相比，HWENO-U格式具有以下优势：(1) 实施过程更简洁——整个流程仅需单次HWENO重构，无需对控制方程进行任何修改；(2) 效率更高——在HWENO限制器和空间重构中使用相同的候选模板、重构多项式及线性和非线性权重；(3) 对问题依赖性降低，合理性增强——函数$u$及其非零倍数$\zeta u$具有相同的非线性权重。此外，该格式保留了现有HWENO格式的紧凑重构模板和人工线性权重等优势。通过大量基准算例验证了所提格式的精度、效率、分辨率和鲁棒性。