Hao Zhang, Yidao Dong, Shichao Zheng null, Xiaogang Deng
{"title":"基于波形识别的不连续检测器和混合WCNS方案分析","authors":"Hao Zhang, Yidao Dong, Shichao Zheng null, Xiaogang Deng","doi":"10.4208/cicp.oa-2023-0080","DOIUrl":null,"url":null,"abstract":". 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.","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":" ","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analysis of Discontinuity Detectors and Hybrid WCNS Schemes Based on Waveform Recognition\",\"authors\":\"Hao Zhang, Yidao Dong, Shichao Zheng null, Xiaogang Deng\",\"doi\":\"10.4208/cicp.oa-2023-0080\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". 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.\",\"PeriodicalId\":50661,\"journal\":{\"name\":\"Communications in Computational Physics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2023-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Computational Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.4208/cicp.oa-2023-0080\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Computational Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.4208/cicp.oa-2023-0080","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
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.
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.