A Cell-Based Smoothed Finite Element Method for Solving Incompressible Reynolds-Averaged Navier–Stokes Equations Using Spalart–Allmaras Turbulence Model

Abstract

In this paper, a leap forward in the development of a cell-based smoothed finite element method (CS-FEM) is presented to solve incompressible turbulent flow treated by Reynolds–averaged Navier–Stokes (RANS) equations and the Spalart–Allmaras (SA) model. The streamline-upwind/Petrov–Galerkin stabilization combined with the stabilized pressure gradient projection (SUPG/SPGP) is used to address oscillation and instability for CS-FEM in calculations of incompressible flow. The capability, accuracy, and validity of presented turbulent CS-FEM were tested by four numerical examples, including turbulent channel flow, a backward-facing step, flow past a circular cylinder, and turbulent flow past multistage Tesla valves. Based on the favorable comparison of numerical results obtained by the presented CS-FEM with experimental results and literature numerical results, CS-FEM is demonstrated to be highly applicable with appealing performances on simulations of incompressible turbulent flows. This new extension of CS-FEM empowers the S-FEM family to solve complex turbulent flows.