  In this paper, a fifth-order Hermite weighted essentially non-oscillatory
(HWENO) scheme with artificial linear weights is proposed for one and two
dimensional hyperbolic conservation laws, where the zeroth-order and the
first-order moments are used in the spatial reconstruction. We construct the
HWENO methodology using a nonlinear convex combination of a high degree
polynomial with several low degree polynomials, and the associated linear
weights can be any artificial positive numbers with only requirement that their
summation equals one. The one advantage of the HWENO scheme is its simplicity
and easy extension to multi-dimension in engineering applications for we can
use any artificial linear weights which are independent on geometry of mesh.
The another advantage is its higher order numerical accuracy using less
candidate stencils for two dimensional problems. In addition, the HWENO scheme
still keeps the compactness as only immediate neighbor information is needed in
the reconstruction and has high efficiency for directly using linear
approximation in the smooth regions. In order to avoid nonphysical oscillations
nearby strong shocks or contact discontinuities, we adopt the thought of
limiter for discontinuous Galerkin method to control the spurious oscillations.
Some benchmark numerical tests are performed to demonstrate the capability of
the proposed scheme.
