  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.
