A cell‐based smoothed finite element method with semi‐implicit CBS procedures for incompressible laminar viscous flows

Abstract

SummaryIn this paper, the cell‐based smoothed finite element method (CS‐FEM) with the semi‐implicit characteristic‐based split (CBS) scheme (CBS/CS‐FEM) is proposed for computational fluid dynamics. The 3‐node triangular (T3) element and 4‐node quadrilateral (Q4) element are used for present CBS/CS‐FEM for two‐dimensional flows. The 8‐node hexahedral element (H8) is used for three‐dimensional flows. Two types of CS‐FEM are implemented in this paper. One is standard CS‐FEM with quadrilateral gradient smoothing cells for Q4 element and hexahedron cells for H8 element. Another is called as n‐sided CS‐FEM (nCS‐FEM) whose gradient smoothing cells are triangles for Q4 element and pyramids for H8 element. To verify the proposed methods, benchmarking problems are tested for two‐dimensional and three‐dimensional flows. The benchmarks show that CBS/CS‐FEM and CBS/nCS‐FEM are capable to solve incompressible laminar flow and can produce reliable results for both steady and unsteady flows. The proposed CBS/CS‐FEM method has merits on better robustness against distorted mesh with only slight more computation time and without losing accuracy, which is important for problems with heavy mesh distortion. The blood flow in carotid bifurcation is also simulated to show capabilities of proposed methods for realistic and complicated flow problems.