Numerical Approach to Energy Minimization of Fluid Configurations Using Phase-Field Models

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dc.contributor.advisorTreinen, Ray
dc.contributor.authorGallo, Erika
dc.contributor.committeeMemberLee, Young Ju
dc.contributor.committeeMemberWang, Chunmei
dc.date.accessioned2018-08-06T14:13:46Z
dc.date.available2018-08-06T14:13:46Z
dc.date.issued2018-08
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 E∈(u) = {Ω (∈|∇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.description.departmentMathematics
dc.formatText
dc.format.extent78 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationGallo, E. (2018). Numerical approach to energy minimization of fluid configurations using phase-field models (Unpublished thesis). Texas State University, San Marcos, Texas.
dc.identifier.urihttps://hdl.handle.net/10877/7367
dc.language.isoen
dc.subjectphase field
dc.subjectfluid configurations
dc.subjectcapillarity
dc.subjectoptimization
dc.subjectenergy minimization
dc.titleNumerical Approach to Energy Minimization of Fluid Configurations Using Phase-Field Models
dc.typeThesis
thesis.degree.departmentMathematics
thesis.degree.disciplineApplied Mathematics
thesis.degree.grantorTexas State University
thesis.degree.levelMasters
thesis.degree.nameMaster of Science

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