Numerical Approach to Energy Minimization of Fluid Configurations Using Phase-Field Models
| dc.contributor.advisor | Treinen, Ray | |
| dc.contributor.author | Gallo, Erika | |
| dc.contributor.committeeMember | Lee, Young Ju | |
| dc.contributor.committeeMember | Wang, Chunmei | |
| dc.date.accessioned | 2018-08-06T14:13:46Z | |
| dc.date.available | 2018-08-06T14:13:46Z | |
| dc.date.issued | 2018-08 | |
| dc.description.abstract | <p>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</p> <p>E∈(u) = {Ω (∈|∇u| + a u (1 − u) + uG(x) + λu dx,</p> <p>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.</p> <p>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.</p> | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 78 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Gallo, E. (2018). <i>Numerical approach to energy minimization of fluid configurations using phase-field models</i> (Unpublished thesis). Texas State University, San Marcos, Texas. | |
| dc.identifier.uri | https://hdl.handle.net/10877/7367 | |
| dc.language.iso | en | |
| dc.subject | Phase field | |
| dc.subject | Fluid configurations | |
| dc.subject | Capillarity | |
| dc.subject | Optimization | |
| dc.subject | Energy minimization | |
| dc.subject.lcsh | Multiphase flow--Mathematical models | en_US |
| dc.subject.lcsh | Fluid dynamics | en_US |
| dc.title | Numerical Approach to Energy Minimization of Fluid Configurations Using Phase-Field Models | |
| dc.type | Thesis | |
| thesis.degree.department | Mathematics | |
| thesis.degree.discipline | Applied Mathematics | |
| thesis.degree.grantor | Texas State University | |
| thesis.degree.level | Masters | |
| thesis.degree.name | Master of Science |
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