A modified fifth-order WENO-Z scheme based on the weights of the reformulated adaptive order WENO scheme

IF 1.7 4区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

International Journal for Numerical Methods in Fluids Pub Date : 2024-06-04 DOI:10.1002/fld.5314

Yize Wang, Kunlei Zhao, Li Yuan

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Abstract

A modified fifth-order WENO-Z scheme is proposed by analogy with the non-normalized weights of the reformulated fifth-order adaptive order (AO) WENO scheme. We show that if the original fifth-order WENO-AO scheme is rewritten as the form of the conventional WENO combination, the resulting non-normalized weights can be divided into three parts: a constant one term, a local stencil smoothness measure term and a global stencil smoothness measure term. In order to make use of the latter two terms for constructing a modified WENO-Z scheme with enhanced performance, we change the form of the third term and introduce an adaptive scaling factor to adjust the contributions from the second and third terms. Numerical examples show that the modified fifth-order WENO-Z scheme has the advantage of high resolution in smooth regions and sharp capturing of discontinuities, and it can obtain evidently better results for shocked flows with small-scale structures compared with the recently developed WENO-Z+ and WENO-Z+M schemes.

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基于重构自适应阶 WENO 方案权重的改进型五阶 WENO-Z 方案

通过类比重新制定的五阶自适应阶次（AO）WENO 方案的非归一化权值，我们提出了一种改进的五阶 WENO-Z 方案。我们的研究表明，如果将原始的五阶 WENO-AO 方案改写成传统 WENO 组合的形式，则所得到的非归一化权重可分为三个部分：常数项、局部模版平滑度测量项和全局模版平滑度测量项。为了利用后两个项构建性能更高的改进型 WENO-Z 方案，我们改变了第三项的形式，并引入了一个自适应缩放因子来调整第二项和第三项的贡献。数值示例表明，修正的五阶 WENO-Z 方案具有对平滑区域分辨率高、对不连续区域捕捉敏锐的优点，与最近开发的 WENO-Z+ 和 WENO-Z+M 方案相比，它在具有小尺度结构的冲击流中可以获得明显更好的结果。

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来源期刊

International Journal for Numerical Methods in Fluids 物理-计算机：跨学科应用

CiteScore

3.70

自引率

5.60%

发文量

111

审稿时长

8 months

期刊介绍： The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction. Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review. The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.