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dc.contributor.advisorTreinen, Ray
dc.contributor.authorGallo, Erika ( )
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 Numerical approach to energy minimization of fluid configurations using phase-field models (Unpublished thesis).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.

We 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.format.extent78 pages
dc.format.medium1 file (.pdf)
dc.subjectPhase field
dc.subjectFluid configurations
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
dc.contributor.committeeMemberLee, Young Ju
dc.contributor.committeeMemberWang, Chunmei Mathematics State University of Science



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