A cell-based smoothed finite element method for incompressible turbulent flows

Abstract

PurposeThe purpose of this paper is to investigate the feasibility of solving turbulent flows based on smoothed finite element method (S-FEM). Then, the differences between S-FEM and finite element method (FEM) in dealing with turbulent flows are compared.Design/methodology/approachThe stabilization scheme, the streamline-upwind/Petrov-Galerkin stabilization is coupled with stabilized pressure gradient projection in the fractional step framework. The Reynolds-averaged Navier-Stokes equations with standard k-epsilon model are selected to solve turbulent flows based on S-FEM and FEM. Standard wall functions are applied to predict boundary layer profiles.FindingsThis paper explores a completely new application of S-FEM on turbulent flows. The adopted stabilization scheme presents a good performance on stabilizing the flows, especially for very high Reynolds numbers flows. An advantage of S-FEM is found in applying wall functions comparing with FEM. The differences between S-FEM and FEM have been investigated.Research limitations/implicationsThe research in this work is limited to the two-dimensional incompressible turbulent flow.Practical implicationsThe verification and validation of a new combination are conducted by several numerical examples. The new combination could be used to deal with more complicated turbulent flows.Social implicationsThe applications of the new combination to study basic and complex turbulent flow are also presented, which demonstrates its potential to solve more turbulent flows in nature and engineering.Originality/valueThis work carries out a great extension of S-FEM in simulations of fluid dynamics. The new combination is verified to be very effective in handling turbulent flows. The performances of S-FEM and FEM on turbulent flows were analyzed by several numerical examples. Superior results were found compared with existing results and experiments. Meanwhile, S-FEM has an advantage of accuracy in predicting boundary layer profile.