{"title":"多孔介质流动中重力指法的行波解。","authors":"K. Mitra, A. Ratz, B. Schweizer","doi":"10.13140/RG.2.2.23096.78083","DOIUrl":null,"url":null,"abstract":"We study an imbibition problem for porous media. When a wetted layer is above a dry medium, gravity leads to the propagation of the water downwards into the medium. In experiments, the occurrence of fingers was observed, a phenomenon that can be described with models that include hysteresis. In the present paper, we describe a single finger in a moving frame and set up a free boundary problem to describe the shape and the motion of one finger that propagates with a constant speed. We show the existence of solutions to the travelling wave problem and investigate the system numerically.","PeriodicalId":8445,"journal":{"name":"arXiv: Analysis of PDEs","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Travelling wave solutions for gravity fingering in porous media flows.\",\"authors\":\"K. Mitra, A. Ratz, B. Schweizer\",\"doi\":\"10.13140/RG.2.2.23096.78083\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study an imbibition problem for porous media. When a wetted layer is above a dry medium, gravity leads to the propagation of the water downwards into the medium. In experiments, the occurrence of fingers was observed, a phenomenon that can be described with models that include hysteresis. In the present paper, we describe a single finger in a moving frame and set up a free boundary problem to describe the shape and the motion of one finger that propagates with a constant speed. We show the existence of solutions to the travelling wave problem and investigate the system numerically.\",\"PeriodicalId\":8445,\"journal\":{\"name\":\"arXiv: Analysis of PDEs\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-11-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Analysis of PDEs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.13140/RG.2.2.23096.78083\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Analysis of PDEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.13140/RG.2.2.23096.78083","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Travelling wave solutions for gravity fingering in porous media flows.
We study an imbibition problem for porous media. When a wetted layer is above a dry medium, gravity leads to the propagation of the water downwards into the medium. In experiments, the occurrence of fingers was observed, a phenomenon that can be described with models that include hysteresis. In the present paper, we describe a single finger in a moving frame and set up a free boundary problem to describe the shape and the motion of one finger that propagates with a constant speed. We show the existence of solutions to the travelling wave problem and investigate the system numerically.
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