The aim of this paper is the presentation of a new modified weighted essentially non-oscillatory scheme with a seventh-order of accuracy, and, a novel nonlinear weighting method. Local smoothness indicators of this scheme constructed using Lagrange’s interpolation polynomial. We developed a new high-order global smoothness indicator, which guarantees the optimal order of accuracy of the scheme at critical points. We used the linear advection equation for verification of the order of accuracy at critical points. Later, we used a series of one- and two-dimensional benchmark problems to verify the shock-capturing capabilities and improved numerical resolution of the new scheme.

本文的目的是介绍一种新的修正加权基本非振荡方案，其精度为七阶，以及一种新颖的非线性加权方法。该方案的局部平滑度指标使用拉格朗日插值多项式构建。我们开发了一个新的高阶全局平滑度指标，它保证了方案在关键点的最佳精度顺序。我们使用线性平流方程来验证关键点的精度顺序。后来，我们使用一系列一维和二维基准问题来验证新方案的冲击捕获能力和改进的数值分辨率。