A segregated finite element solution for non-isothermal flow

Abstract

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 non-symmetric 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. Three cases are used as a basis for the study, i.e. the flow in a square cavity, the flow between parallel plates and natural convection in a square cavity. The effect that the choice of the values of the relaxation parameters has on the number of iterations which is needed to obtain a converged solution is investigated. In each case there is an optimum combination which is amongst others a function of the grid and the flow parameters. A non-optimum choice may lead either to an unnecessary number of iterations or the solution becoming unstable. From the results it is concluded that the method performs well when the optimum combination of the values for the relaxation parameters is used. However, much can still be done to improve the robustness of the method.