In this article, we introduce a new method which allows utilizing all the available sub-stencils of a WENO scheme to increase the accuracy of the numerical solution of conservation laws while preserving the non-oscillatory property of the scheme. In this method, near a discontinuity, if there is a smooth sub-stencil with higher-order of accuracy, it is used in the reconstruction procedure. Furthermore, in smooth regions, all the sub-stencils of the same order of accuracy form the stencil with the highest order of accuracy as the conventional WENO scheme. The presented method is assessed using several test cases of the linear wave equation and one- and two-dimensional Euler's equations of gas dynamics. In addition to the original weights of WENO schemes, the WENO-Z approach is used. The results show that the new method increases the accuracy of the results while properly maintaining the ENO property.

翻译：本文提出一种新方法，该方法允许利用WENO格式所有可用的子模板来提高守恒律数值解的精度，同时保持格式的非振荡特性。在该方法中，在间断附近，若存在具有更高阶精度的光滑子模板，则将其用于重构过程。此外，在光滑区域，所有相同阶精度的子模板构成具有最高阶精度的模板，这与传统WENO格式相同。通过线性波动方程以及一维和二维气体动力学欧拉方程的多个测试算例对所提方法进行评估。除WENO格式原始权重外，还采用了WENO-Z方法。结果表明，新方法在适当保持ENO特性的同时提高了结果的精度。