The weighted essentially non-oscillatory schemes are well known for their shock captu- ring abilities due to their properties resulting from weighted combination reconstruction taken such that less weight is given to less smooth stencils. In this article, contrary to this property, the analysis has been done by adding extra weight to less smooth substencils of the domain that in turn adds the useful information which plays a vital role in improving resolution of the solution mainly at discontinuities or sharp gradients. The theoretical aspects have been supported with scalar, one-dimensional as well as two-dimensional test problems for third- and fifth-order schemes. Numerical solutions obtained by the proposed third-order scheme are comparable to the numerical solutions obtained using some of the native fifth-order WENO schemes.

加权的基本非振荡方案以其震荡能力而闻名，这是由于其加权组合重建所带来的性能，使得对较不光滑的模板给予较少的加权。在本文中，与该属性相反，已通过对域的较不光滑子集增加额外的权重来进行分析，而子集又增加了有用的信息，这些信息对提高解决方案的分辨率至关重要，主要是在不连续或陡峭的梯度下。理论方面得到了三阶和五阶方案的标量，一维和二维测试问题的支持。通过提议的三阶方案获得的数值解与使用某些本机五阶WENO方案获得的数值解可比。