N-S方程基于投影法的特征线算子分裂有限元求解

提出了一种求解非定常不可压缩纳维-斯托克斯方程（N-S方程）的新型有限元法:基于投影法的特征线算子分裂有限元法.在每一个时间层上将N-S方程分裂成扩散项、对流项、压力修正项.对流项采用多步显式格式，且在每一个对流子时间步内采用更加精确的显式特征线-伽辽金法进行时间离散，空间离散采用标准伽辽金法.应用此算法对平面泊肃叶流、方腔流和圆柱绕流进行数值模拟，所得结果与基准解符合良好.尤其对于Re=10000的方腔流，给出了方腔中分离涡发展和运动的计算结果，并发现在该雷诺数下存在周期解，表明该算法能较好地模拟流体流动中的小尺度物理量以及流场中分离涡的运动. 

NUMERICAL SIMULATION FOR NAVIER-STOKES EQUATIONS BY PROJECTION/CHARACTERISTIC-BASED OPERATOR-SPLITTING FINITE ELEMENT METHOD

A novel finite element method, which is projection/Characteristic-based operator-splitting finite element method, is proposed for the prediction of unsteady incompressible N-S equations. In each time step, the equations are split into the diffusive part, the convective part and the pressure correction part. The temporal discretization of the convective part is performed by an exact characteristic-Galerkin method. The convective part is solved explicitly and a multistep technique is introduced to enlarge the calculation precision. The plane Poisseuille flow, the driven square flow and the flow over a circular cylinder are conducted to validate the model. It is show that the numerical results are close to reference results. In particularly, for the driven square flow at Re=10000, the flow becomes periodical in time and small vortex structure can be simulated.