A stabilized reduced integration cell-based smoothed finite element method for incompressible laminar flow

In this work, a cell-based smoothed finite element method (CS-FEM) empowered by reduced integration (CS-RI) is proposed to more efficiently solve incompressible laminar flow problems than previous CS-FEM. The proposed method incorporates the characteristic-based split scheme to deal with pressure check-board and hourglass control for instability caused by reduced integration. The reduced integration techniques can significantly save computational costs by treating each four-node quadrilateral (Q4) element or eight-node hexahedral (H8) element as a single smoothing domain (SD). However, previous CS-FEM takes 4 SDs for Q4 element and 6 (or 8) SDs for H8 element, respectively. Through carefully selected two-dimensional (2D) and three-dimensional (3D) benchmark examples, the stability, accuracy, and efficiency of the proposed CS-RI method are compared with reference results and original CS-FEM. The results show that the proposed method can substantially improve the computational speed while still maintaining comparable accuracy and stability, making it particularly promising for fluid dynamics applications.