Bidimensional modeling for incompressible viscous flow using the Circumcenter Based Approach in an unstructured grid

Abstract

A possible approach for modeling two-dimensional convection-diffusion problems in a cell-centered scheme with an unstructured triangular grid is the use of the Circumcenter, that is the center of the circumference that passes through the vertices of the triangular volume. This point is used to calculate all variables involved in the numerical simulation, and a Finite Volume Method was use to discretize the equations of an Incompressible Viscous Flow. This work analyzes classical problems of bidimensional flow, such as the inlet region of a Poiseuille flow, lid-driven cavity, backward-facing step and free convection with Boussinesq approximation. The application of the method has been shown to be a simple and flexible scheme and the results fit the analytical, experimental or numeric data presented in the literature.