On the resolution of the viscous incompressible flow for various SUPG finite element formulations

Abstract

[Abstract] A Finite Element based program has been released to solve the steady 2D Navier- Stokes equations. The mixed-variable algorithm is used as a first approach to solve the differential problem. In order to reduce the number of equations, both a penalty and segregated formulation are implemented to give solution to the viscous incompressible flow and their results are compared with the former formulation. The program makes use of a SUPG type algorithm as a stabilisation procedure, in order to eliminate the numerical oscillations, which may appear when the boundary conditions force a sudden change in the solution, without necessarily refining the mesh. The three different algorithms are checked making use of the benchmark problems of the flow in a square cavity, the backward step and the flow past a cylinder. Finally the code is used to solve the flow in some practical problems and their results are commented.