{"data":{"id":"10.4231/r7mk69tv","type":"dois","attributes":{"doi":"10.4231/r7mk69tv","prefix":"10.4231","suffix":"r7mk69tv","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Dong, Suchuan","givenName":"Suchuan","familyName":"Dong","affiliation":["Purdue University"],"nameIdentifiers":[{"schemeUri":"https://orcid.org","nameIdentifier":"https://orcid.org/0000-0001-6778-0679","nameIdentifierScheme":"ORCID"}]}],"titles":[{"title":"Two-Phase Outflows: Boundary Conditions and Algorithm"}],"publisher":"Purdue University Research Repository","container":{},"publicationYear":2014,"subjects":[{"subject":"multiphase flow"},{"subject":"two-phase flow"},{"subject":"Mathematics"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"outflow boundary condition"},{"subject":"open boundary condition"},{"subject":"two-phase outflow"},{"subject":"inflow boundary condition"},{"subject":"phase field method"},{"subject":"two-phase open boundary"},{"subject":"large density ratio"},{"subject":"variable coefficient matrix"},{"subject":"spectral element method"},{"subject":"Physics"}],"contributors":[],"dates":[{"date":"2014-06-16","dateType":"Available"},{"date":"2014-06-16","dateType":"Submitted"},{"date":"2014-06-19","dateType":"Accepted"},{"date":"2014","dateType":"Issued"}],"language":"en","types":{"ris":"DATA","bibtex":"misc","citeproc":"dataset","schemaOrg":"Dataset","resourceType":"Datasets","resourceTypeGeneral":"Dataset"},"relatedIdentifiers":[{"relationType":"References","relatedIdentifier":"10.1016/j.jcp.2014.02.011","resourceTypeGeneral":"JournalArticle","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":["14 files","9 MB"],"formats":["image/jpeg","application/pdf"],"version":"1.0","rightsList":[{"rights":"Creative Commons Attribution Non Commercial 3.0 Unported","rightsUri":"https://creativecommons.org/licenses/by-nc/3.0/legalcode","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"cc-by-nc-3.0","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"\u0026lt;p\u0026gt;We present an effective outflow boundary condition,\u0026amp;nbsp;and an associated numerical algorithm, within the phase-field\u0026amp;nbsp;framework for dealing with two-phase outflows or\u0026amp;nbsp;open boundaries.\u0026amp;nbsp;The set of two-phase outflow boundary conditions for the phase-field\u0026amp;nbsp;and flow variables are designed to prevent the un-controlled growth in the total\u0026amp;nbsp;energy of the two-phase system, even in situations\u0026amp;nbsp;where strong backflows or vortices may be\u0026amp;nbsp;present\u0026amp;nbsp;at the outflow\u0026amp;nbsp; boundaries.\u0026amp;nbsp;We also present an additional boundary condition\u0026amp;nbsp;for the phase field function, which together\u0026amp;nbsp;with the usual Dirichlet condition can\u0026amp;nbsp;work effectively as the phase-field inflow\u0026amp;nbsp;conditions.\u0026amp;nbsp;The numerical algorithm for dealing with these boundary\u0026amp;nbsp;conditions is developed on top of a strategy for de-coupling the computations\u0026amp;nbsp;of all flow variables and for\u0026amp;nbsp;overcoming the performance bottleneck\u0026amp;nbsp;caused by variable\u0026amp;nbsp;coefficient matrices associated with variable\u0026amp;nbsp;density/viscosity.\u0026amp;nbsp;The algorithm contains special constructions,\u0026amp;nbsp;for treating the variable dynamic viscosity in the outflow boundary condition, and for\u0026amp;nbsp;preventing a numerical locking at the outflow boundaries\u0026amp;nbsp;for time-dependent problems.\u0026amp;nbsp;Extensive numerical tests \u0026amp;nbsp;with incompressible two-phase flows involving\u0026amp;nbsp;inflow and outflow boundaries\u0026amp;nbsp;demonstrate that, the\u0026amp;nbsp;two-phase outflow\u0026amp;nbsp;boundary conditions and the numerical algorithm\u0026amp;nbsp;developed herein allow for the fluid interface and the \u0026amp;nbsp;two-phase flow to pass through the outflow\u0026amp;nbsp;or open boundaries in a smooth and seamless\u0026amp;nbsp;fashion,\u0026amp;nbsp;and that our method produces stable\u0026amp;nbsp; simulations\u0026amp;nbsp;when large density ratios and\u0026amp;nbsp;large viscosity ratios are involved\u0026amp;nbsp;and when strong backflows are\u0026amp;nbsp;present at the outflow boundaries.\u0026lt;/p\u0026gt;","descriptionType":"Abstract"},{"description":"We present an effective outflow boundary condition, and an associated numerical algorithm, within the phase field framework for dealing with two-phase outflows or open boundaries.","descriptionType":"Other"}],"geoLocations":[],"fundingReferences":[{"awardTitle":"Joint Diagonalization-Based Spectral Element 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