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| Author(s): |
Pedro Alexandre da Cruz
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2011-08-04 |
| Examining board members: |
Murilo Francisco Tomé;
Rosário Elida Suman Bretas;
Antonio Castelo Filho;
Gilmar Mompean Munhoz da Cruz;
Sérgio Luiz Frey
|
| Advisor: | Murilo Francisco Tomé |
| Abstract | |
The aim of this work is to develop numerical methods capable of simulating nematic liquid crystal flows described by the dynamic Ericksen-Leslie equations. Two numerical techniques have been proposed: a numerical method for solving three-dimensional flows of nematic liquid crystals under strong magnetic fields and a method for simulating flows of nematic liquid crystals in two-dimensional complex geometries. Both methods employ Cartesian coordinates using primitive variables of pressure and velocity. These techniques are based on the GENSMAC (GENeralized-Simplified-Marker-And-Cell) methodology and a detailed description of the equations involved is presented. The resulting governing equations are solved by the finite difference method on a staggered grid. The three-dimensional technique was applied to solve fully developed flow between two paralel plates for which an analytic solution exists. By using this analytic solution, validation and convergence results of the developed numerical technique were obtained. To validate the two-dimensional method developed herein, an analytic solution for steady state flow in a 2D-channel was found which was used to obtain validation and convergence results. The method was then applied to simulate the flow in L-shaped channels, flow through a 4:1 contraction and flow in a 4:1 expansion (AU) | |
| FAPESP's process: | 07/07038-2 - Numerical solution nematic liquid crystal |
| Grantee: | Pedro Alexandre da Cruz |
| Support Opportunities: | Scholarships in Brazil - Doctorate |