Improvement of multistep WENO scheme and its extension to higher orders of accuracy
Improvement of multistep WENO scheme and its extension to higher orders of accuracy
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DOI：
10.1002/fld.4242
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发表时间：
2016-12
影响因子：
1.8
通讯作者：
Yankai Ma;Zhen-Guo Yan;Huajun Zhu
中科院分区：
文献类型：
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作者：
Yankai Ma;Zhen-Guo Yan;Huajun Zhu
本文提出了一种有效的方法来克服不连续点附近加权基本非振荡格式的缺陷。通过将平滑性指标彻底纳入权重定义，设计出高达九阶的精确多步方法，提供加权基本非振荡方案，在从光滑区域到不连续的过渡点具有增强的收敛顺序，同时保持稳定性和基本非振荡行为。我们还提供了对分辨率的详细分析，并表明新方法在光滑区域的解决增强来自于它们使平滑指标更接近均匀性的能力。新方案具有与其他多步骤方案相似的保真度；但是，由于不需要逻辑语句或映射函数，因此在鲁棒性和效率方面具有优越的特性。向更高精度的扩展不会带来额外的复杂性。采用线性平流问题和非线性双曲守恒律的数值解来证明该方案在激波捕获问题上的改进行为。版权所有©2016 John Wiley & Sons， Ltd。
This paper presents an efficient procedure for overcoming the deficiency of weighted essentially non‐oscillatory schemes near discontinuities. Through a thorough incorporation of smoothness indicators into the weights definition, up to ninth‐order accurate multistep methods are devised, providing weighted essentially non‐oscillatory schemes with enhanced order of convergence at transition points from smooth regions to a discontinuity, while maintaining stability and the essentially non‐oscillatory behavior. We also provide a detailed analysis of the resolution power and show that the solution enhancements of the new method at smooth regions come from their ability to render smoothness indicators closer to uniformity. The new scheme exhibits similar fidelity as other multistep schemes; however, with superior characteristics in terms of robustness and efficiency, as no logical statements or mapping function is needed. Extensions to higher orders of accuracy present no extra complexity. Numerical solutions of linear advection problems and nonlinear hyperbolic conservation laws are used to demonstrate the scheme's improved behavior for shock‐capturing problems. Copyright © 2016 John Wiley & Sons, Ltd.