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dc.contributor.advisorTreinen, Ray
dc.contributor.authorGallo, Erika
dc.date.accessioned2018-08-06T14:13:46Z
dc.date.available2018-08-06T14:13:46Z
dc.date.issued2018-07-23
dc.date.submittedAugust 2018
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/7367
dc.description.abstractWe consider a fluid, under isothermal conditions and confined to a bounded container of homogeneous makeup, whose Gibbs free energy, per unit volume, is a prescribed function of its density distribution. Based on the Van der Waals-Cahn-Hilliard Theory of phase transitions, we minimize our functional, whose phase field formulation is obtained by considering an energy of the type EE(u) = {Ω (E|∇u| + a u (1 − u) + uG(x) + λu dx, where u is the phase function, G is a potential energy, and λ represents volume constraint. We know that these minimizers, EE, as E goes to 0, will Γ−converge to the minimizer of the capillary energy functional. Although numerical approaches to this minimization exists, current approaches are unable to distinguish between local and global minimizers of the functional. I propose a mesh-grid-based optimization approach, with Dirichlet boundary conditions. Assuming convexity of our system, we utilize a logarithmic barrier optimization scheme in hopes to guarantee convergence to the global minimum of our energy functional.
dc.formatText
dc.format.extent78 pages
dc.format.medium1 file (.pdf)
dc.language.isoen_US
dc.subjectPhase Field
dc.subjectFluid Configurations
dc.subjectCapillarity
dc.subjectOptimization
dc.subjectEnergy Minimization
dc.subject.lcshMultiphase flow--Mathematical modelsen_US
dc.subject.lcshFluid dynamicsen_US
dc.titleNumerical Approach to Energy Minimization of Fluid Configurations Using Phase-Field Models
txstate.documenttypeThesis
dc.contributor.committeeMemberLee, Young Ju
dc.contributor.committeeMemberWang, Chunmei
thesis.degree.departmentMathematics
thesis.degree.disciplineApplied Mathematics
thesis.degree.grantorTexas State University
thesis.degree.levelMasters
thesis.degree.nameMaster of Science
txstate.departmentMathematics


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