  A novel central weighted essentially non-oscillatory (central WENO;
CWENO)-type scheme for the construction of high-resolution approximations to
discontinuous solutions to hyperbolic systems of conservation laws is
presented. This procedure is based on the construction of a global average
weight using the whole set of Jiang-Shu smoothness indicators associated to
every candidate stencil. By this device one does not to have to rely on ideal
weights, which, under certain stencil arrangements and interpolating point
locations, do not define a convex combination of the lower-degree interpolating
polynomials of the corresponding sub-stencils. Moreover, this procedure also
prevents some cases of accuracy loss near smooth extrema that are experienced
by classical WENO and CWENO schemes. These properties result in a more flexible
scheme that overcomes these issues, at the cost of only a few additional
computations with respect to classical WENO schemes and with a smaller cost
than classical CWENO schemes. Numerical examples illustrate that the proposed
CWENO schemes outperform both the traditional WENO and the original CWENO
schemes.
