Two Different Formulations for Solving the Navier- Stokes Equations with Moderate and High Reynolds Numbers

In this work, we discuss the numerical solution of the Taylor vortex and the lid-driven cavity problems. Both problems are solved using the Stream function-vorticity formula- tion of the Navier-Stokes equations in 2D. Results are obtained using a fixed point iterative method and working with matrixes A and B resulting from the discretization of the Laplacian and the advective term, respectively. We solved both problems with Reynolds numbers in the range of 3200 ≤ Re ≤ 7500. Results are also obtained using the velocity-vorticity formulation of the Navier-Stokes equations. In this case, we are using only the fixed point iterative method. We present results for the lid-driven cavity prob- lem and for the Stream function-vorticity formulation with Reynolds numbers in the range of 3200 ≤ Re ≤ 7500. As the Reynolds number increases, the time and the space step size have to be refined. We show results for 3200 ≤ Re ≤ 20,000. The numerical scheme with the velocity-vorticity formulation uses a smaller step size for both time and space. Results are not as good as with the Stream function-vorticity formulation, although the way the scheme behaves gives us another point of view on the behavior of fluids under different numerical schemes and different formulation.

• Tipo de recurso: Book
• Fecha de publicación: 2021
• Institución: Universidad de Bogotá Jorge Tadeo Lozano
• Repositorio: Expeditio: repositorio UTadeo
• Idioma: eng
• OAI Identifier: oai:expeditiorepositorio.utadeo.edu.co:20.500.12010/16715
• Acceso en línea: https://www.intechopen.com/books/computational-fluid-dynamics-basic-instruments-and-applications-in-science/two-different-formulations-for-solving-the-navier-stokes-equations-with-moderate-and-high-reynolds-n; http://hdl.handle.net/20.500.12010/16715
• Palabra clave: Ecuaciones de Navier - Stokes; Formulación de velocidad vorticidad; Número de Reynolds; Formulación de función de flujo vorticidad
• License: Abierto (Texto Completo)