Characteristic-Based Operator-Splitting Finite Element Method For Navier-Stokes Equations

There are many problems which concerned with fluid motion in engineering field and Navier-Stokes(N-S) equations are fundamental dominating equations to describe fluid motion. The numerical solution of the N-S equations which is a difficult problem in Computational Fluid Dynamics(CFD) ever since has significant meaning for CFD even for Engineering.A new finite element method, which is the characteristic-based operator-splitting(CBOS) algorithm, is presented in the paper for the solution of the N-S equations. In each time step, the N-S equations are split into the diffusive part and the convective part by adopting the operator-splitting algorithm. For the diffusive part, the time discretization is based on the backward difference method which yields an implicit scheme and the spatial discretization is performed by the standard Galerkin method. The convective part can be discretized using the characteristic Galerkin method and solved explicitly.This coupled numerical method takes the advantage of both the operator-splitting algorithm and the characteristic-based Galerkin method. The equations'diffusive character and convection dominated property are both considered by the operator-splitting algorithm, and the difficulty of solving big scale of nonlinear equations on the whole flow domain is also avoid. The standard Galerkin method is adopted to solve the diffusive part whose result is treated as the initial value of the convective part. The simple explicit characteristic Galerkin method which is referenced from the CBS method for discrete the convective part yields an additional diffusive term along the streamline. The detail processes of the discretization of both two parts are given as well.The driven cavity flow, backward-facing step flow and single cylinder flow are conducted to validate the model, and it turns out that the numerical results agree well with the standard solutions or existing experimental data, indicating that the model has good accuracy and high stability, and it provides a promising research method for the solution of the N-S equations.