  In this paper, A new sixth-order weighted essentially non-oscillatory (WENO)
scheme, refered as the WENO-6, is proposed in the finite volume framework for
the hyperbolic conservation laws. Instead of selecting one stencil for each
cell in the classical WENO scheme [10], two independent stencils are used for
two ends of the considering cell in the current approach. Meanwhile, the
stencils, which are used for the reconstruction of variables at both sides of
interface, are symmetrical. Compared with the classical WENO scheme [10], the
current WENO scheme achieves one order of improvement in accuracy with the same
stencil. The reconstruction procedure is defined by a convex combination of
reconstructed values at cell interface, which are constructed from two
quadratic and two cubic polynomials. The essentially non-oscillatory property
is achieved by the similar weighting methodology as the classical WENO scheme.
A variety of numerical examples are presented to validate the accuracy and
robustness of the current scheme.
