Linear and Nonlinear Analyses of the Onset of Buoyancy-Induced Instability in an Unbounded Porous Medium Saturated by Miscible Fluids
This study analyzes the stability of an initially sharp interface between two miscible fluids in a porous medium. Linear stability equations are first derived using the similarity variable of the basic state, and then transformed into a system of ordinary differential equations using a spectral expa...
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| Veröffentlicht in: | Transport in porous media 2014-09, Vol.104 (2), p.407-433 |
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| creator | Kim, Min Chan Yadav, Dhananjay |
| description | This study analyzes the stability of an initially sharp interface between two miscible fluids in a porous medium. Linear stability equations are first derived using the similarity variable of the basic state, and then transformed into a system of ordinary differential equations using a spectral expansion with and without quasi-steady-state approximation (QSSA). These transformed equations are solved using the eigenanalysis and initial value problem approach. The initial growth rate analysis shows that initially the system is unconditionally stable. The stability characteristics obtained under the present QSSA are quantitatively same as those obtained without the QSSA. To support these theoretical results, numerical simulations are conducted using the Fourier-spectral method. The results of theoretical linear stability analyses and the numerical simulations validate to each other. |
| doi_str_mv | 10.1007/s11242-014-0341-4 |
| format | Article |
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Linear stability equations are first derived using the similarity variable of the basic state, and then transformed into a system of ordinary differential equations using a spectral expansion with and without quasi-steady-state approximation (QSSA). These transformed equations are solved using the eigenanalysis and initial value problem approach. The initial growth rate analysis shows that initially the system is unconditionally stable. The stability characteristics obtained under the present QSSA are quantitatively same as those obtained without the QSSA. To support these theoretical results, numerical simulations are conducted using the Fourier-spectral method. The results of theoretical linear stability analyses and the numerical simulations validate to each other.</description><identifier>ISSN: 0169-3913</identifier><identifier>EISSN: 1573-1634</identifier><identifier>DOI: 10.1007/s11242-014-0341-4</identifier><identifier>CODEN: TPMEEI</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Boundary value problems ; Civil Engineering ; Classical and Continuum Physics ; Computational fluid dynamics ; Computer simulation ; Differential equations ; Earth and Environmental Science ; Earth Sciences ; Earth, ocean, space ; Engineering and environment geology. Geothermics ; Exact sciences and technology ; Geotechnical Engineering & Applied Earth Sciences ; Hydrocarbons ; Hydrogeology ; Hydrology. 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Linear stability equations are first derived using the similarity variable of the basic state, and then transformed into a system of ordinary differential equations using a spectral expansion with and without quasi-steady-state approximation (QSSA). These transformed equations are solved using the eigenanalysis and initial value problem approach. The initial growth rate analysis shows that initially the system is unconditionally stable. The stability characteristics obtained under the present QSSA are quantitatively same as those obtained without the QSSA. To support these theoretical results, numerical simulations are conducted using the Fourier-spectral method. The results of theoretical linear stability analyses and the numerical simulations validate to each other.</description><subject>Boundary value problems</subject><subject>Civil Engineering</subject><subject>Classical and Continuum Physics</subject><subject>Computational fluid dynamics</subject><subject>Computer simulation</subject><subject>Differential equations</subject><subject>Earth and Environmental Science</subject><subject>Earth Sciences</subject><subject>Earth, ocean, space</subject><subject>Engineering and environment geology. Geothermics</subject><subject>Exact sciences and technology</subject><subject>Geotechnical Engineering & Applied Earth Sciences</subject><subject>Hydrocarbons</subject><subject>Hydrogeology</subject><subject>Hydrology. Hydrogeology</subject><subject>Hydrology/Water Resources</subject><subject>Industrial Chemistry/Chemical Engineering</subject><subject>Interface stability</subject><subject>Mathematical analysis</subject><subject>Miscibility</subject><subject>Nonlinear analysis</subject><subject>Ordinary differential equations</subject><subject>Pollution, environment geology</subject><subject>Porous media</subject><subject>Sedimentary rocks</subject><subject>Spectral methods</subject><subject>Stability analysis</subject><issn>0169-3913</issn><issn>1573-1634</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp1kM1u1TAQhSMEEpfCA7CzhFgaxr_JXZaKwpVuKRJ0bdmxA65Su3jiRR6A98ZXqeiqi9FoPOccjb-ue8vgAwPoPyJjXHIKTFIQklH5rNsx1QvKtJDPux0wvadiz8TL7hXiLUBzDXLX_T3GFGwhNnnyLad5m86TnVcMSPJElt-BXCcMy2n4VPNq07jSQ_J1DJ4cEi7WxTkuK4mpxZCb5HJNvu2-55IrkqvgY70jP-xSi13au1vJVcQxujmQy7lGj6-7F5OdMbx56GfdzeXnnxdf6fH6y-Hi_EitBL5Q7XSY5OBs77nS2odejNxLNjGl-cCt6wEUV8z5VsFqpfSeAxsAwIEbB3HWvdty70v-UwMu5jbX0j6LhgspFXDFTyq2qcaSEUuYzH2Jd7ashoE50TYbbdNomxNtI5vn_UOyxdHOU2mUIv438kHveyX6puObDtsq_Qrl8YKnw_8Bp0yPDg</recordid><startdate>20140901</startdate><enddate>20140901</enddate><creator>Kim, Min Chan</creator><creator>Yadav, Dhananjay</creator><general>Springer Netherlands</general><general>Springer</general><general>Springer Nature B.V</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>D1I</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>KB.</scope><scope>L6V</scope><scope>M7S</scope><scope>PDBOC</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20140901</creationdate><title>Linear and Nonlinear Analyses of the Onset of Buoyancy-Induced Instability in an Unbounded Porous Medium Saturated by Miscible Fluids</title><author>Kim, Min Chan ; Yadav, Dhananjay</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a402t-6b6ef48ba7d2566de73c2d41f156282ab7005251bd51bea655692018000b0bc83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Boundary value problems</topic><topic>Civil Engineering</topic><topic>Classical and Continuum Physics</topic><topic>Computational fluid dynamics</topic><topic>Computer simulation</topic><topic>Differential equations</topic><topic>Earth and Environmental Science</topic><topic>Earth Sciences</topic><topic>Earth, ocean, space</topic><topic>Engineering and environment geology. Geothermics</topic><topic>Exact sciences and technology</topic><topic>Geotechnical Engineering & Applied Earth Sciences</topic><topic>Hydrocarbons</topic><topic>Hydrogeology</topic><topic>Hydrology. Hydrogeology</topic><topic>Hydrology/Water Resources</topic><topic>Industrial Chemistry/Chemical Engineering</topic><topic>Interface stability</topic><topic>Mathematical analysis</topic><topic>Miscibility</topic><topic>Nonlinear analysis</topic><topic>Ordinary differential equations</topic><topic>Pollution, environment geology</topic><topic>Porous media</topic><topic>Sedimentary rocks</topic><topic>Spectral methods</topic><topic>Stability analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kim, Min Chan</creatorcontrib><creatorcontrib>Yadav, Dhananjay</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Materials Science Collection</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>Materials Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Materials Science Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><jtitle>Transport in porous media</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kim, Min Chan</au><au>Yadav, Dhananjay</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Linear and Nonlinear Analyses of the Onset of Buoyancy-Induced Instability in an Unbounded Porous Medium Saturated by Miscible Fluids</atitle><jtitle>Transport in porous media</jtitle><stitle>Transp Porous Med</stitle><date>2014-09-01</date><risdate>2014</risdate><volume>104</volume><issue>2</issue><spage>407</spage><epage>433</epage><pages>407-433</pages><issn>0169-3913</issn><eissn>1573-1634</eissn><coden>TPMEEI</coden><abstract>This study analyzes the stability of an initially sharp interface between two miscible fluids in a porous medium. 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| subjects | Boundary value problems Civil Engineering Classical and Continuum Physics Computational fluid dynamics Computer simulation Differential equations Earth and Environmental Science Earth Sciences Earth, ocean, space Engineering and environment geology. Geothermics Exact sciences and technology Geotechnical Engineering & Applied Earth Sciences Hydrocarbons Hydrogeology Hydrology. Hydrogeology Hydrology/Water Resources Industrial Chemistry/Chemical Engineering Interface stability Mathematical analysis Miscibility Nonlinear analysis Ordinary differential equations Pollution, environment geology Porous media Sedimentary rocks Spectral methods Stability analysis |
| title | Linear and Nonlinear Analyses of the Onset of Buoyancy-Induced Instability in an Unbounded Porous Medium Saturated by Miscible Fluids |
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