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

• Published in: International journal for numerical methods in fluids 2018-01, Vol.86 (1), p.20-45
• Main Authors: Jiang, Chen, Zhang, Zhi‐Qian, Han, Xu, Liu, Guirong, Lin, Tao
• Format: Article
• Language: English
• Subjects: Benchmarks; Bifurcations; Blood; Blood flow; Carotid artery; Cells; cell‐based gradient smoothing; Computation; Computational fluid dynamics; Computer applications; Computer simulation; CS‐FEM; Dynamics; Finite element analysis; Finite element method; Fluid dynamics; Fluid flow; Hydrodynamics; Incompressible flow; Laminar flow; Mathematical analysis; Nonlinear programming; Procedures; Pyramids; Robustness (mathematics); semi‐implicit CBS; Smoothing; Three dimensional flow; Triangles; Two dimensional flow
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.4406

Summary In 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. The cell‐based smoothing finite element method (CS‐FEM) is first applied to solve the incompressible laminar flow. Two types of CS‐FEM for both 2D and 3D flows are implemented. Since gradient smoothing technique is used, the iso‐parametric mapping is circumvented. Numerical tests for several benchmarks demonstrate CS‐FEM is able to deal with laminar flows and show better robustness than FEM. Blood flow in carotid bifurcation has been simulated by present method to exhibit its application for complex flow problem.