基于波形识别的不连续检测器和混合WCNS方案分析

IF 2.6 3区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Communications in Computational Physics Pub Date : 2023-06-01 DOI:10.4208/cicp.oa-2023-0080
Hao Zhang, Yidao Dong, Shichao Zheng null, Xiaogang Deng
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引用次数: 0

摘要

在本文中,我们分别应用线性和非线性方法对光滑和不连续区域,提出了双曲守恒律的加权紧致非线性格式(WCNS)的混合形式。要实现该算法,离不开所采用的不连续检测器的识别能力。具体而言,故障单元指示器用于识别不平滑区域,如冲击波和接触不连续性,同时避免对平滑结构的误判。一些经典的检测器分为三种基本类型:导数组合、光滑度指标和特征分解。同时,提出了一种新的改进检测器进行比较。然后通过识别一系列波形对其进行分析。之后,使用欧拉方程对使用这些指标以及不同检测变量的混合方案进行了检验,以研究它们在不同水平上区分实际不连续性的能力。仿真结果表明,该算法具有与纯WCNS相似的性能,而对于1D情况,该算法通常节省50%的CPU时间,对于2D Euler方程,该算法节省约40%的CPU时间。目前的研究希望为判断现有的不连续检测器和开发新的不连续性检测器提供一些参考和建立一些标准。
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Analysis of Discontinuity Detectors and Hybrid WCNS Schemes Based on Waveform Recognition
. In this paper, we present a hybrid form of weighted compact nonlinear scheme (WCNS) for hyperbolic conservation laws by applying linear and nonlinear methods for smooth and discontinuous zones individually. To fulfill this algorithm, it is inseparable from the recognition ability of the discontinuity detector adopted. In specific, a troubled-cell indicator is utilized to recognize unsmooth areas such as shock waves and contact discontinuities, while avoiding misjudgments of smooth structures. Some classical detectors are classified into three basic types: derivative combination, smoothness indicators and characteristic decomposition. Meanwhile, a new improved detector is proposed for comparison. Then they are analyzed through identifying a series of waveforms firstly. After that, hybrid schemes using such indicators, as well as different detection variables, are examined with Euler equations, so as to investigate their ability to distinguish practical discontinuities on various levels. Simulation results demonstrate that the proposed algorithm has similar performances to pure WCNS, while it generally saves 50 percent of CPU time for 1D cases and about 40 percent for 2D Euler equations. Current research is in the hope of providing some reference and establishing some standards for judging existing discontinuity detectors and developing novel ones.
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来源期刊
Communications in Computational Physics
Communications in Computational Physics 物理-物理:数学物理
CiteScore
4.70
自引率
5.40%
发文量
84
审稿时长
9 months
期刊介绍: Communications in Computational Physics (CiCP) publishes original research and survey papers of high scientific value in computational modeling of physical problems. Results in multi-physics and multi-scale innovative computational methods and modeling in all physical sciences will be featured.
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