A numerical algorithm using a bilinear or linear finite element and semi-implicit three-step method is presented for the analysis of incompressible viscous fluid problems. The streamline upwind/Petrov-Galerkin (SUPG) ...A numerical algorithm using a bilinear or linear finite element and semi-implicit three-step method is presented for the analysis of incompressible viscous fluid problems. The streamline upwind/Petrov-Galerkin (SUPG) stabilization scheme is used for the formulation of the Navier-Stokes equations. For the spatial discretization, the convection term is treated explicitly, while the viscous term is treated implicitly, and for the temporal discretization, a three-step method is employed. The present method is applied to simulate the lid driven cavity problems with different geometries at low and high Reynolds numbers. The results compared with other numerical experiments are found to be feasible and satisfactory.展开更多
基金Supported by State Key Program of National Natural Science Foundation of China （60834001） and National Natural Science Foundation of China （60774022）.Acknowledgement Authors would like to thank NSFC organizers and participants who shared their ideas and works with us during the NSFC workshop on data-based control, decision making, scheduling, and fault diagnosis. In particular, authors would like to thank Chai Tian-You, Sun You-Xian, Wang Hong, Yan Hong-Sheng, and Gao Fu-Rong for discussing the concept on design model shown in Fig. 12, the concept on temporal multi-scale shown in Fig. 8, the concept on fault diagnosis shown in Fig. 14, the concept on dynamic scheduling shown in Fig. 15, and the concept on interval model shown in Fig. 16, respectively.
基金Project supported by the National Natural Science Foundation of China (No.51078230)the Research Fund for the Doctoral Program of Higher Education of China (No.200802480056)the Key Project of Fund of Science and Technology Development of Shanghai (No.10JC1407900),China
文摘A numerical algorithm using a bilinear or linear finite element and semi-implicit three-step method is presented for the analysis of incompressible viscous fluid problems. The streamline upwind/Petrov-Galerkin (SUPG) stabilization scheme is used for the formulation of the Navier-Stokes equations. For the spatial discretization, the convection term is treated explicitly, while the viscous term is treated implicitly, and for the temporal discretization, a three-step method is employed. The present method is applied to simulate the lid driven cavity problems with different geometries at low and high Reynolds numbers. The results compared with other numerical experiments are found to be feasible and satisfactory.
