{"title":"Labyrinthine Pattern Formation in Magnetic Liquids","authors":"A. Cēbers, I. Drikis","doi":"10.1201/9780203755518-2","DOIUrl":"https://doi.org/10.1201/9780203755518-2","url":null,"abstract":"","PeriodicalId":12357,"journal":{"name":"Free boundary problems:","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77095502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-11DOI: 10.1201/9780203755518-14
C. Lederman, N. Wolanski
{"title":"Limit, Pointwise, Viscosity and Classical Solutions to a Free Boundary Problem in Combustion","authors":"C. Lederman, N. Wolanski","doi":"10.1201/9780203755518-14","DOIUrl":"https://doi.org/10.1201/9780203755518-14","url":null,"abstract":"","PeriodicalId":12357,"journal":{"name":"Free boundary problems:","volume":"70 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77843435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-11DOI: 10.1201/9780203755518-10
M. Guedda, D. Hilhorst, M. Peletier
{"title":"Blow-Up of Interfaces for an Inhomogeneous Aquifer","authors":"M. Guedda, D. Hilhorst, M. Peletier","doi":"10.1201/9780203755518-10","DOIUrl":"https://doi.org/10.1201/9780203755518-10","url":null,"abstract":"","PeriodicalId":12357,"journal":{"name":"Free boundary problems:","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87819414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, the ow of uids in porous media is studied as a free or moving boundary problem by the mixed method. In particular, a new weak formulation for the problem of seepage of uids through a porous media is discussed and analyzed mathematically and numerically. The new formulation is in a mixed form and is suitable for the use of mixed nite element methods in the numerical approximation. It is proved that the weak formulation and its nite element discretization has a solution which can be approximated by a sequence of regularized problems. 1. Introduction In this paper, we are concerned with the free or moving boundary value problem in the study of the ow of uids through a heterogeneous porous media. Such problems are important in many branches of science and engineering. For example, in the areas of soil science, agricultural engineering , and groundwater hydrology, the movement of uids and their dissolved components in both saturated and unsaturated soils is an important environmental consideration. In petroleum engineering, improved recovery of oil and gas is based on simulation of multiphase and multicomponent uid transport in deep rocks. In both application areas, mass transfer across phase boundaries is an important consideration which can be discussed in the context of free or moving boundary problems. Another important application of the free or moving boundary problem is water seepage through a dam, or rain water creeping through an unsatu-rated zone. The underlying physics of the petroleum and seepage problems are very similar. For comparison, assume that there are two uids owing simultaneously in the porous medium. In unsaturated ow, these uids are water and air, while in the petroleum problem, the uids are assumed to be water and oil. Relevant material properties, including the capillary pressure and relative permeability are assumed to be known. Free boundary problems are also seen in other areas of petroleum industry such as basin simulation. The research of basin simulation is important
{"title":"A Study of Free Boundary Problems of Fluid Flow in Porous Media by Mixed Methods","authors":"L. Badea, R. Ewing, J. Wang","doi":"10.1201/9780203755518-1","DOIUrl":"https://doi.org/10.1201/9780203755518-1","url":null,"abstract":"In this article, the ow of uids in porous media is studied as a free or moving boundary problem by the mixed method. In particular, a new weak formulation for the problem of seepage of uids through a porous media is discussed and analyzed mathematically and numerically. The new formulation is in a mixed form and is suitable for the use of mixed nite element methods in the numerical approximation. It is proved that the weak formulation and its nite element discretization has a solution which can be approximated by a sequence of regularized problems. 1. Introduction In this paper, we are concerned with the free or moving boundary value problem in the study of the ow of uids through a heterogeneous porous media. Such problems are important in many branches of science and engineering. For example, in the areas of soil science, agricultural engineering , and groundwater hydrology, the movement of uids and their dissolved components in both saturated and unsaturated soils is an important environmental consideration. In petroleum engineering, improved recovery of oil and gas is based on simulation of multiphase and multicomponent uid transport in deep rocks. In both application areas, mass transfer across phase boundaries is an important consideration which can be discussed in the context of free or moving boundary problems. Another important application of the free or moving boundary problem is water seepage through a dam, or rain water creeping through an unsatu-rated zone. The underlying physics of the petroleum and seepage problems are very similar. For comparison, assume that there are two uids owing simultaneously in the porous medium. In unsaturated ow, these uids are water and air, while in the petroleum problem, the uids are assumed to be water and oil. Relevant material properties, including the capillary pressure and relative permeability are assumed to be known. Free boundary problems are also seen in other areas of petroleum industry such as basin simulation. The research of basin simulation is important","PeriodicalId":12357,"journal":{"name":"Free boundary problems:","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87331765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-11DOI: 10.1201/9780203755518-19
J. Lowengrub, J. Goodman, H. Lee, E. Longmire, M. Shelley, L. Truskinovsky
A set of fundamental yet ill understood phenomena in uid dynamics involves changes in the topology of interfaces between partially miscible or nominally immiscible uids Such changes occur for example when continuous jets pinch o into droplets when sheared interfaces atomize and when droplets of one uid reconnect with one another These topological transitions occur in many practical applications involving transport mixing and separation of petroleum chemical and food products as well as contaminated waste streams The dynamics of topological transitions are di cult to understand and model for several reasons For one the uids in which these transitions occur are complex A second problem associated with topological transitions is caused by the short time scales over which they occur In practical ows the transition time scales are much shorter than the local ow time scales making the transitions di cult to characterize experimentally or compute numerically A third problem associated with transitions is purely numerical how does one handle the change in interface topology in a physically justi ed way In this paper we will address the last problem in the context of incompressible uid ows Many researchers see for example have tried using ad hoc methods to change the topology of interfaces While this approach often referred to as contour surgery allows topological transitions to be overcome it is di cult to justify the reconnection conditions based on physical principles In a few special cases involving uid gas interfaces it is possible to develop physically based reconnection conditions by using special similarity solutions of the Navier Stokes equations see For ows involving liquid liquid interfaces however the dynamics are more complicated and no such similarity solutions have been constructed
{"title":"Topological Transitions in Liquid/Liquid Interfaces","authors":"J. Lowengrub, J. Goodman, H. Lee, E. Longmire, M. Shelley, L. Truskinovsky","doi":"10.1201/9780203755518-19","DOIUrl":"https://doi.org/10.1201/9780203755518-19","url":null,"abstract":"A set of fundamental yet ill understood phenomena in uid dynamics involves changes in the topology of interfaces between partially miscible or nominally immiscible uids Such changes occur for example when continuous jets pinch o into droplets when sheared interfaces atomize and when droplets of one uid reconnect with one another These topological transitions occur in many practical applications involving transport mixing and separation of petroleum chemical and food products as well as contaminated waste streams The dynamics of topological transitions are di cult to understand and model for several reasons For one the uids in which these transitions occur are complex A second problem associated with topological transitions is caused by the short time scales over which they occur In practical ows the transition time scales are much shorter than the local ow time scales making the transitions di cult to characterize experimentally or compute numerically A third problem associated with transitions is purely numerical how does one handle the change in interface topology in a physically justi ed way In this paper we will address the last problem in the context of incompressible uid ows Many researchers see for example have tried using ad hoc methods to change the topology of interfaces While this approach often referred to as contour surgery allows topological transitions to be overcome it is di cult to justify the reconnection conditions based on physical principles In a few special cases involving uid gas interfaces it is possible to develop physically based reconnection conditions by using special similarity solutions of the Navier Stokes equations see For ows involving liquid liquid interfaces however the dynamics are more complicated and no such similarity solutions have been constructed","PeriodicalId":12357,"journal":{"name":"Free boundary problems:","volume":"02 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86473074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-11DOI: 10.1201/9780203755518-13
M. Korten
{"title":"On a Structure Theorem for Some Free Boundary Problems for the Heat Equation","authors":"M. Korten","doi":"10.1201/9780203755518-13","DOIUrl":"https://doi.org/10.1201/9780203755518-13","url":null,"abstract":"","PeriodicalId":12357,"journal":{"name":"Free boundary problems:","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72704373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-11DOI: 10.1201/9780203755518-21
A. Wagner
{"title":"On the Bernoulli Free Boundary Problem with Surface Tension","authors":"A. Wagner","doi":"10.1201/9780203755518-21","DOIUrl":"https://doi.org/10.1201/9780203755518-21","url":null,"abstract":"","PeriodicalId":12357,"journal":{"name":"Free boundary problems:","volume":"73 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75632224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-11DOI: 10.1201/9780203755518-15
L. Antanovskii, R. Grimshaw
{"title":"Hysteresis Behaviour of a Pointed Drop in Taylor’s Four-Roller Mill","authors":"L. Antanovskii, R. Grimshaw","doi":"10.1201/9780203755518-15","DOIUrl":"https://doi.org/10.1201/9780203755518-15","url":null,"abstract":"","PeriodicalId":12357,"journal":{"name":"Free boundary problems:","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90283672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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