不可压缩粘性流动的CBS有限元解法

对于二维不可压缩粘性流动,首先通过坐标变换的方式得到了的不含对流项的NS方程,并给出了CBS有限元方法求解的一般过程。结合一类同时含有压力和速度的出口边界条件,对方腔顶盖驱动流、后向台阶绕流和圆柱绕流进行了计算。所得结果与基准解符合良好,验证了CBS算法对于定常、非定常粘性不可压缩流动问题的可行性和所用出口边界条件的无反射特性。特别的,对于圆柱绕流,Re=100时非定常升、阻力系数及漩涡脱落等非定常都得到了较好地模拟,为一进步研究自激振动等更加复杂的非定常流动问题奠定了基础。

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, a good 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.