On the application of the CBS finite element method to the incompressible flow

A finite element method for the incompressible flow,the Characteristic-Based Split(CBS)algorithm,is presented in this paper.First,the convective term of the incompressible Navier-Stokes(NS) equation is eliminated via a coordinate transformation,and then the calculation procedure of CBS algorithm is presented.Combined with a type of outflow boundary condition,typical problems of the incompressible flow including the lid-driven flow in a square cavity,flow over a backward-facing step and the flow past a circular cylinder are calculated.Numerical results from CBS are compared with the benchmark solutions,and a good agreement is achieved.Especially,for the flow past a circular cylinder at Re=100,agood simulation of the unsteady phenomena such as the oscillatory coefficients of lift and drag and the vortex shedding are achieved,which lays a solid foundation for the further study of flow problems such as the flow-induced vibration.