论文标题
非线性退化抛物线方程的六阶中央WENO方案
A sixth-order central WENO scheme for nonlinear degenerate parabolic equations
论文作者
论文摘要
在本文中，我们开发了一种新的六阶有限差中央加权基本上非振荡（WENO）方案，具有Z型非线性权重，用于非线性退化抛物线方程。为了避免负线性重量，引入了中心的多项式。我们根据$ l^2 $ -NORM平滑度指示器选择Z型非线性权重，以更准确的分辨率产生新的WENO方案。还可以证实，所提出的具有设计的非线性权重的中央WENO方案在平滑区域达到了第六阶的精度。提出了一维数值示例，以证明拟议的中央WENO方案的性能提高。
In this paper we develop a new sixth-order finite difference central weighted essentially non-oscillatory (WENO) scheme with Z-type nonlinear weights for nonlinear degenerate parabolic equations. The centered polynomial is introduced for the WENO reconstruction in order to avoid the negative linear weights. We choose the Z-type nonlinear weights based on the $L^2$-norm smoothness indicators, yielding the new WENO scheme with more accurate resolution. It is also confirmed that the proposed central WENO scheme with the devised nonlinear weights achieves sixth order accuracy in smooth regions. One- and two-dimensional numerical examples are presented to demonstrate the improved performance of the proposed central WENO scheme.
