A Finite element formulation for the resolution of the unsteady incompressible viscous flow for low Reynolds numbers

Abstract

[Abstract] The following paper shows a Finite Element formulation for the resolution of the local and convective acceleration terms including- Navier-Stokes equations, which gives analytical response to the problem of viscous, incompressible, unsteady flows. The integration of the resulting non-linear system of first order ordinary differential equations, is made upon a successive approximation algorithm together with an implicit backward time integrating scheme. The interpolation of the spatial domain is made in terms of a Q1/P0 pair (bilinear velocity-constant pressure). The usage of a Bubnov Galerkin formulation in the process of obtaining a weak form implies that flows of a certain velocity need the employment of a very refined spatial mesh so as to avoid numerical instability. For high Reynolds numbers the convection term becomes predominant compared to the diffussion term and a different algorithm (SPGU, GLS), should be introduced. Finally the developed program is checked over some of the most commonly used flow tests and its results on velocity and pressure are shown.