A Segregated Finite Element Approach to the Solution of the Navier-stokes Equations for Incompressible Flow

A segregated finite element algorithm for the solution of the SUPG formulation of the incompressible steady-state Navier-Stokes equations for non-isothermal flow is presented in this paper. The method features equal order interpolation for all the flow variables. The SIMPLER and SIMPLEST algorithms are employed and the sets of nonsymmetric linear equations are solved by means of the preconditioned conjugate gradient squared solver, whilst the preconditioned conjugate gradient solver is used to solve the sets of symmetric linear equations. The effect of the value of the Euclidian norm to test for the convergence of the solution is investigated. It is shown that the Euclidian norm is grid dependent. Also the effect of applying the SUPG weighting functions to all the terms in the momentum and energy equations is compared with the effect of applying the functions to the convective terms only. Three cases are investigated, i.e. the flow in a square cavity, the flow between parallel plates and natural convection in a square cavity. In the case of the driven cavity flow the full SUPG formulation results in a grid independent solution being reached sooner. However, in the case of the flow between parallel plates this is not necessarily the case. The problem is attributed to the weighting of the pressure terms in the momentum equations. It is concluded that this needs thorough investigation.