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

Abstract

Abstract 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.