A. Salnikov, A. Akhmetzianov, A. Kushner, V. Lychagin
{"title":"构造演化过滤方程吸引子的一种数值方法","authors":"A. Salnikov, A. Akhmetzianov, A. Kushner, V. Lychagin","doi":"10.1109/SUMMA48161.2019.8947585","DOIUrl":null,"url":null,"abstract":"A numerical method is proposed to construct attractors of evolution equations describing the process of filtration of a two-phase liquid with allowance for capillary forces (the Rapoport-Leas model). The stability conditions for the proposed method are the conditions under which the third-order dynamics is an attractor for the initial equation. The solution of the initial equation is an iterative process, which can be paralleled to accelerate calculations.","PeriodicalId":163496,"journal":{"name":"2019 1st International Conference on Control Systems, Mathematical Modelling, Automation and Energy Efficiency (SUMMA)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"A Numerical Method for Constructing Attractors of Evolutionary Filtration Equations\",\"authors\":\"A. Salnikov, A. Akhmetzianov, A. Kushner, V. Lychagin\",\"doi\":\"10.1109/SUMMA48161.2019.8947585\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A numerical method is proposed to construct attractors of evolution equations describing the process of filtration of a two-phase liquid with allowance for capillary forces (the Rapoport-Leas model). The stability conditions for the proposed method are the conditions under which the third-order dynamics is an attractor for the initial equation. The solution of the initial equation is an iterative process, which can be paralleled to accelerate calculations.\",\"PeriodicalId\":163496,\"journal\":{\"name\":\"2019 1st International Conference on Control Systems, Mathematical Modelling, Automation and Energy Efficiency (SUMMA)\",\"volume\":\"43 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2019 1st International Conference on Control Systems, Mathematical Modelling, Automation and Energy Efficiency (SUMMA)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/SUMMA48161.2019.8947585\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2019 1st International Conference on Control Systems, Mathematical Modelling, Automation and Energy Efficiency (SUMMA)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SUMMA48161.2019.8947585","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Numerical Method for Constructing Attractors of Evolutionary Filtration Equations
A numerical method is proposed to construct attractors of evolution equations describing the process of filtration of a two-phase liquid with allowance for capillary forces (the Rapoport-Leas model). The stability conditions for the proposed method are the conditions under which the third-order dynamics is an attractor for the initial equation. The solution of the initial equation is an iterative process, which can be paralleled to accelerate calculations.
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