A monolithic method for solving the incompressible Navier-Stokes equations

• Grant number: 13/18819-6
• Support type: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): November 01, 2013
• Effective date (End): July 31, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Cassio Machiaveli Oishi
• Grantee: Hugo Leonardo França
• Home 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

In this project, we will analyze a monolithic method for solving the incompressible Navier-Stokes equations. In the context of MAC (Marker-And-Cell) finite difference method and staggered grids, we will investigate the discretization process applied in the coupled formulation. In particular, we will study strategies to treat the non-linear terms in the governing equations, and we will analyse Krylov subspace methods for the iterative solution of the linear system. We will assess the developed method for two-dimensional problems, for instance, the Poiseuille flow and the driven cavity flow. Finally, in the context of computational efficiency and accuracy, we will perform a comparative study between the monolithic and projection methods.