Study of matrix decompositions applied to incompressible viscoelastic flows

• Grant number: 12/02517-8
• Support Opportunities: Scholarships in Brazil - Master
• Start date: June 01, 2012
• End date: February 28, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Cassio Machiaveli Oishi
• Grantee: Irineu Lopes Palhares Junior
• Host Institution: Faculdade de Ciências e Tecnologia (FCT). Universidade Estadual Paulista (UNESP). Campus de Presidente Prudente. Presidente Prudente , SP, Brazil
• Associated research grant: 09/15892-9 - Study of stable and accurate numerical methods for transient flows: improvements, implementations, free surface flow problems and viscoelastic models, AP.JP

Abstract

One difficulty in the solution of complex viscoelastic flows occurs when numerical instabilities arise in the simulation. These instabilities result in a breakdown of numerical schemes used for solving the constitutive equation for non-Newtonian fluids. This difficulty is known as the High Weissenberg Number Problem. In order to avoid these instabilities, matrix decompositions have been applied on the conformation tensor A. In this project we will study some decompositions applied to this tensor which is symmetric and defined positive. Firstly, we will re-write the constitutive equation of the Oldroyd-B model in terms of the conformation tensor A. After this, in the context of the ``Marker-and-Cell'' method, the Navier-Stokes and the constitutive equations will be solved via projection method. Finally, the numerical techniques will be tested for solving two-dimensional incompressible flows. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

PALHARES JUNIOR, Irineu Lopes. Decomposições matriciais para escoamentos viscoelásticos incompressíveis. 2014. Master's Dissertation - Universidade Estadual Paulista (Unesp). Faculdade de Ciências e Tecnologia. Presidente Prudente Presidente Prudente.