A cell-based smoothed finite element method (CS-FEM) for three-dimensional incompressible laminar flows using mixed wedge-hexahedral element. (1st December 2021)

• Record Type: Journal Article
• Authors: Liu, Mingyang; Gao, Guangjun; Zhu, Huifen; Jiang, Chen; Liu, Guirong
• Is Part Of: Engineering analysis with boundary elements. Volume 133(2021)
• Page Start: 269
• Page End: 285
• Publication Date: 2021-12-01
• Subjects: Smoothed finite element method (S-FEM) -- Streamline-upwind/Petrov-Galerkin stabilization (SUPG) -- Stabilized pressure gradient projection (SPGP) -- Incompressible flow -- Laminar flow -- Three-dimension; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2021.09.008
• Languages: English
• ISSNs: 0955-7997

Abstract

Highlights: A novel extension of smoothed finite element method (S-FEM) to solve three-dimensional incompressible flows. The computational efficiency and computational accuracy of the hexahedral element, wedge elements and mixed wedge-hexahedral elements were compared. Analysis of performance of S-FEM on three-dimensional incompressible flows. It is feasible in solving three-dimensional incompressible flow problems by the present method. 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+.