A Cell-Based Smoothed Finite Element Model for the Analysis of Turbulent Flow Using Realizable K-Ε Model and Mixed Meshes

Smoothed finite element method (S-FEM) has been widely employed in computational mechanics, particularly in computational solid mechanics (CSM) and, to a lesser extent, in computational fluid dynamics (CFD). The present work focuses on the development of S-FEM for solving threedimensional incompressible turbulent flow problems using the realizable k-epsilon model. The Streamline Upwind Petrov-Galerkin approach combined with Stabilized Pressure Gradient Projection (SUPG/SPGP) was used to restrain/control the spatial oscillation and instability in conjunction with mixed meshes employed to discretize complex geometries. The presented turbulent cell-based S-FEM (CS-FEM) was validated under several common flow types, including mesh turbulence, turbulent channel flow, turbulent flow past a circular cylinder, flow separation around an obstacle, flow in the dimpled channel, and flow in the upper human airway. In particular, the presented work exhibited the latent capability of the CS-FEM in solving turbulent flows near boundary regions and strong convection regions. Meanwhile, the results of the CS-FEM were compared to those of the lowest equal-order finite element method (i.e. P1-P1 or Q1-Q1 elements) in simulating turbulent flows, and it was found that the CS-FEM had better agreement with other published works.