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五阶精度、基于矩并采用统一次模板的Hermite加权本质无振荡格式（简称HWENO-U）。该格式的核心思想是：仅利用空间重构的相同信息，在时间离散中通过HWENO限制器修正一阶矩；该限制器不仅能有效抑制伪振荡，还能确保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，该权重仅包含解的积分平均值，在保留原始权重所有性质的同时，对求解具有剧烈尺度变化的挑战性问题更具鲁棒性。与现有HWENO格式相比，HWENO-U格式具有以下优势：（1）实施过程更简单，整个流程中仅需应用一次HWENO重构，无需对控制方程进行任何修改；（2）通过在HWENO限制器和空间重构中采用相同的候选模板、重构多项式以及线性和非线性权重，提高了计算效率；（3）由于函数$u$及其非零倍数$\zeta u$具有相同的非线性权重，因此减少了问题依赖性，提升了合理性。此外，该格式保留了现有HWENO格式的优点，包括紧凑的重构模板和人工线性权重的使用。我们通过大量基准算例验证了该格式的精度、效率、分辨率和鲁棒性。