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.

翻译：本文提出了一种新型中心加权本质无振荡（central WENO；CWENO）格式，用于构造双曲守恒律方程组间断解的高分辨率近似。该方法通过利用与每个候选模板相关的全部江-舒光滑度指标来构造全局平均权重。通过这一手段，无需依赖理想权重——在某些模板排列和插值点位置下，理想权重无法定义对应子模板的低次插值多项式的凸组合。此外，该方法还避免了经典WENO和CWENO格式在光滑极值附近出现的部分精度损失情况。这些特性使得该格式更加灵活，克服了上述问题，且相对于经典WENO格式仅需少量额外计算，其计算成本低于经典CWENO格式。数值算例表明，所提出的CWENO格式优于传统WENO格式和原始CWENO格式。