{"title":"Development of an optimal adaptive finite element stabiliser for the simulation of complex flows","authors":"","doi":"10.1016/j.sciaf.2024.e02311","DOIUrl":null,"url":null,"abstract":"<div><p>An optimal adaptive multiscale finite element method(AMsFEM) for numerical solutions of flow problems modelled by the Oldroyd B model is developed. Complex flows experience instabilities due to a phenomena known as the high Weissenberg number problem. The stabilisers are terms in-cooperated into the variational formulation when applying the finite element method. For the selected few stabilisers, numerical experiments are performed to study the convergence of the solutions. These demonstrate that adaptive strategies reduce the computational load of flow simulation. A best performing combination of choice of stabiliser and adaptive strategy is suggested.</p></div>","PeriodicalId":21690,"journal":{"name":"Scientific African","volume":null,"pages":null},"PeriodicalIF":2.7000,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2468227624002552/pdfft?md5=a15a837bb5f1cc93c09739b6a4f3b315&pid=1-s2.0-S2468227624002552-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Scientific African","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2468227624002552","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0
Abstract
An optimal adaptive multiscale finite element method(AMsFEM) for numerical solutions of flow problems modelled by the Oldroyd B model is developed. Complex flows experience instabilities due to a phenomena known as the high Weissenberg number problem. The stabilisers are terms in-cooperated into the variational formulation when applying the finite element method. For the selected few stabilisers, numerical experiments are performed to study the convergence of the solutions. These demonstrate that adaptive strategies reduce the computational load of flow simulation. A best performing combination of choice of stabiliser and adaptive strategy is suggested.
开发了一种优化自适应多尺度有限元方法(AMsFEM),用于以 Oldroyd B 模型为模型的流动问题的数值求解。由于高韦森伯格数问题这一现象,复杂流动会出现不稳定性。在应用有限元方法时,稳定器是与变分公式相结合的术语。针对选定的几个稳定器,进行了数值实验,以研究解的收敛性。结果表明,自适应策略可减少流动模拟的计算负荷。建议选择性能最佳的稳定器和自适应策略组合。