A cell-based smoothed finite element method (CS-FEM) for three-dimensional incompressible laminar flows using mixed wedge-hexahedral element

Abstract

Smoothed finite element method (S-FEM) has attracted lots of attentions in the fields of computational mechanics, especially in solid mechanics and heat transfer problems. In computational fluid dynamics, works on S-FEM were limited to two-dimensional problems. This work aims to extend the S-FEM to three-dimensional (3D) incompressible laminar flows. Wedge element grids and grids with mixed wedge and hexahedral elements are formulated for 3D incompressible laminar flows based on the cell-based S-FEM (CS-FEM). To reduce numerical oscillations, we implemented the streamline-upwind/Petrov-Galerkin method (SUPG) together with the stabilized pressure gradient projection (SPGP). Several examples are presented, including the Beltrami flow, lid-driven cavity flow, backward facing step flow and microchannel flow, to validate and examine the presented method. The results indicate that wedge elements and mixed wedge-hexahedral elements based on the CS-FEM have higher computational efficiency than that of hexahedral elements based on the CS-FEM for the same level of computational accuracy. It is also found that the present CS-FEM performed better than the standard FEM in dealing with pressure stability. The flow characteristics are well captured by the CS-FEM using the mixed wedge-hexahedral elements, and the numerical results are acceptable compared to those of STAR-CCM+.