Insight into the cell-based smoothed finite element method for convection-dominated flows

• Published in: Computers & structures Vol. 212; pp. 215 - 224
• Main Author: He, Tao
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.02.2019; Elsevier BV
• Subjects: Cell-based smoothed finite element method; Computational fluid dynamics; Convection; Convection-dominated flow; Finite element analysis; Finite element method; Fluid–structure interaction; Gradient smoothing; Mapping; Mathematical analysis; Navier–Stokes; Nonlinear programming; Numerical integration; Quadrilaterals; Smoothing; Navier–Stokes; Fluid–structure interaction; Cell-based smoothed finite element method; Gradient smoothing; Convection-dominated flow
• ISSN: 0045-7949; 1879-2243
• DOI: 10.1016/j.compstruc.2018.10.021

•For the first time, CS-FEM is proved to be naturally applicable to convection-dominated flows.•The cell-based gradient smoothing procedure for the NS equations is arbitrary within smoothing cells.•The center of Q4 element is simplest and may be optimal at element level for numerical integration.•Two smoothing schemes are proposed to evaluate the fluid forces.•The method is free of isoparametric mapping and is advantageous to distorted-mesh problems. This paper unveils an innate ability of the cell-based smoothed finite element method to settle convection-dominated flows. The gradient smoothing procedure for the Navier–Stokes equations is proved arbitrary within smoothing cells (SCs). As a result, previously proposed treatments are automatically compatible with this finding. For numerical integration using four SCs, the center of quadrilateral element is suggested as it is simplest and optimal at element level. Based on the cell-based definition, two smoothing schemes are also proposed to evaluate the fluid forces. The method is accordingly free of isoparametric mapping and accepts severely distorted elements. Competitive results are presented for popular benchmark problems.